וְיֵשׁ דֵּעוֹת שֶׁאָסוּר לוֹ לָאָדָם לִנְהֹג בָּהֶן בְּבֵינוֹנִית אֶלָּא יִתְרַחֵק מִן הַקָּצֶה הָאֶחָד עַד הַקָּצֶה הָאַחֵר...וְכֵן הַכַּעַס מִדָּה רָעָה הִיא עַד לִמְאֹד וְרָאוּי לָאָדָם שֶׁיִּתְרַחֵק מִמֶּנָּה עַד הַקָּצֶה הָאַחֵר. וִילַמֵּד עַצְמוֹ שֶׁלֹּא יִכְעֹס וַאֲפִלּוּ עַל דָּבָר שֶׁרָאוּי לִכְעֹס עָלָיו.
And, yet, there are certain tendencies which man is forbidden to follow in the middle-way, but must distance himself from extreme to extreme... So is anger an extremely evil tendency and it is proper for man to remove himself from it to the other extreme. One should teach himself not to get angry, even over a matter which befits anger.
Let's look at three specific situations. We'll come back to them later on and reanalyze.
The first one is the scene at the burning bush. G-d and Moshe have conversation about Moshe going back to Egypt and delivering the Jews. Moshe is very hesitant, but G-d addresses each of his fears. Until, Moshe states that he has a speech impediment. All of a sudden, G-d gets angry with him. Why?
(14) The LORD became angry with Moses, and He said, “There is your brother Aaron the Levite. He, I know, speaks readily. Even now he is setting out to meet you, and he will be happy to see you.

Going back to the first source, Rambam does mention that is a person needs to impress upon someone, he can appear angry. It can not come from a place of anger, but a person can use a facade of anger as a tool to teach a lesson.
...וְאִם רָצָה לְהַטִּיל אֵימָה עַל בָּנָיו וּבְנֵי בֵּיתוֹ אוֹ עַל הַצִּבּוּר אִם הָיָה פַּרְנָס וְרָצָה לִכְעֹס עֲלֵיהֶן כְּדֵי שֶׁיַּחְזְרוּ לַמּוּטָב יַרְאֶה עַצְמוֹ בִּפְנֵיהֶם שֶׁהוּא כּוֹעֵס כְּדֵי לְיַסְּרָם וְתִהְיֶה דַּעְתּוֹ מְיֻשֶּׁבֶת בֵּינוֹ לְבֵין עַצְמוֹ כְּאָדָם שֶׁהוּא מְדַמֶּה כּוֹעֵס בִּשְׁעַת כַּעֲסוֹ וְהוּא אֵינוֹ כּוֹעֵס. אָמְרוּ חֲכָמִים הָרִאשׁוֹנִים כָּל הַכּוֹעֵס כְּאִלּוּ עוֹבֵד עֲבוֹדַת כּוֹכָבִים. וְאָמְרוּ שֶׁכָּל הַכּוֹעֵס אִם חָכָם הוּא חָכְמָתוֹ מִסְתַּלֶּקֶת מִמֶּנּוּ וְאִם נָבִיא הוּא נְבוּאָתוֹ מִסְתַּלֶּקֶת מִמֶּנּוּ. וּבַעֲלֵי כַּעַס אֵין חַיֵּיהֶם חַיִּים. לְפִיכָךְ צִוּוּ לְהִתְרַחֵק מִן הַכַּעַס עַד שֶׁיַּנְהִיג עַצְמוֹ שֶׁלֹּא יַרְגִּישׁ אֲפִלּוּ לַדְּבָרִים הַמַּכְעִיסִים וְזוֹ הִיא הַדֶּרֶךְ הַטּוֹבָה. וְדֶרֶךְ הַצַּדִּיקִים הֵן עֲלוּבִין וְאֵינָן עוֹלְבִין שׁוֹמְעִים חֶרְפָּתָם וְאֵינָם מְשִׁיבִין עוֹשִׂין מֵאַהֲבָה וּשְׂמֵחִים בְּיִסּוּרִים. וַעֲלֵיהֶם הַכָּתוּב אוֹמֵר (שופטים ה לא) "וְאֹהֲבָיו כְּצֵאת הַשֶּׁמֶשׁ בִּגְבֻרָתוֹ":
...If one desires to engender awe in his children and his household, or in the public, if he be at the head of a community, even if he desire to get angry at them so as to bring them back to the good way, he should only act angry in their presence so as to reprove them, but his disposition must remain calm within himself, even as a man imitates, who is angry when the time calls forth anger but in reality he is not angry. The sages of yore said: "He who yields to anger is as if he worshiped idolatry". They also said: "Whosoever yields to anger, if he be a wise man his wisdom leaves him, and if he be a prophet his prophecy leaves him." Verily the life of irritable persons is no life. They have, therefore, commanded to be afar from anger, so that one will train himself not to mind even the things which do cause irritation, for such is the good way. The conduct of the just is to take insults but not give insults, hear themselves flouted but make no reply, do their duty as a work of love, and bear affliction cheerfully. Concerning them the Verse says: "But may those that love Him be as the rising of the sun in his might" (Judg. 5.31).
The Gemara answers: It is only necessary to discuss this in a case where one does so to instill fear in the members of his household. It is like the incident where Rav Yehuda sought to display his anger and he pulled threads off his garment. Rav Aḥa bar Ya’akov smashed broken vessels, Rav Sheshet threw small fish on his maidservant’s head, and Rabbi Abba broke the lid of a jug. All of these Sages caused minimal damage in creating the impression that they were angry.
An example that I learned from one of my teachers. He is a father of eight children, so he has quite some experience. He said that sometimes his youngest, gets into a fight with another sibling or friend, and his son becomes angry. In truth, it's over something petty and insignificant, and it's almost cute; my teacher needs to stop himself from almost laughing at times. However, it's very serious to his son, so in order to discipline him and help resolve the situation, my teacher must put on a facade of seriousness, and almost and anger of sorts. His other children even mention it to him sometimes, how can he be so angry when the situation is so funny? My teacher responds that of course he isn't angry, but out of a place of love and understanding, he uses this so his son understands that he too is taking the situation seriously.
As we said before, "flaring nostrils" isn't anger, but it is a clear indicator of anger. You look at someone falling their nostrils, and you know they're angry. or at least, they're trying to appear as angry.
A place where we see this in Torah with humans is in the Yosef story, where Yosef is accused of sleeping with Potifar's wife. Potifar "flares his nostrils".
(יט) וַיְהִי֩ כִשְׁמֹ֨עַ אֲדֹנָ֜יו אֶת־דִּבְרֵ֣י אִשְׁתּ֗וֹ אֲשֶׁ֨ר דִּבְּרָ֤ה אֵלָיו֙ לֵאמֹ֔ר כַּדְּבָרִ֣ים הָאֵ֔לֶּה עָ֥שָׂה לִ֖י עַבְדֶּ֑ךָ וַיִּ֖חַר אַפּֽוֹ׃
ואין ספק שאדוניו של יוסף למה שראה שי"י אתו לא האמין לדברי אשתו שאם היה מאמין היה ראוי שיהרגהו אבל עכ"פ הנה התפעל מזה ושמו בבית הסוהר שאם לא היה עושה זה היה לבוז בהיות אשתו אומר' כן ואם היה מחריש היה נותן לה לב לזנו' תחתיו. וז"א ויהי כשמוע אדוניו את דברי אשתו כי לא התפעל מהמעשה לפי שלא האמינו ולא ג"כ מהבגד שנמצא בידה כי אין ספק ששאל את יוסף ושהוא ספר לו האמת אלא שהתורה קצרה בזה להיותו מבואר מכח המסופר. לכן לא אמר ויחר אפו על יוסף אלא ויחר אפו בלבד כי חרה אפו במה שדברה אשתו ומה לעשות לה ואשתו אומרת כך היה הדבר ולכן חשב לשומו בבית הסוהר שהי' הסוהר מתחת ידו ובביתו לשבת שם עד יעבור זעם.
Undoubtedly, when Joseph’s master, appreciating that God was ever-present in his mind, did not believe what his wife was saying; for had he done so, he would have had to put him to death. However, he was still troubled by this episode, and accordingly put him in prison – had he not acted in this way, he would have become a laughing-stock, as his wife was (already) saying as much. By remaining silent, he would have provided her with a pretext for being unfaithful to him. This, then, is what Scripture intends to convey by the phrase, ‘And when his master heard the words of his wife’ (39:19): – for he was not unduly affected by the incident itself, since he lent it no credence; nor was he influenced by the robe found in her hand – as he undoubtedly questioned Joseph about it, and was told the truth. The Torah mentions this only briefly, as it is quite clear from the basic drift of the narrative. Hence it does not say (39:19): ‘And his fury was aroused against Joseph’, but simply, ‘his fury was aroused’. He was angered by what his wife had said, and his mind pre-occupied with what to do to appease her, given that she was insisting on her version of events. Accordingly, he resolved to incarcerate Joseph in the prison-house, which was under his control and located within the precincts of his own home, to remain there until (his wife’s) fury had subsided.
In this example, Moshe is insecure about his speech. So G-d but's on this facade of anger, shows Himself in this more human form, and comforts him. It's ok Moshe, you're brother can speak of you.
וַיֹּאמֶר ... וַיֹּאמֶר אָנֹכִי אֱלֹהֵי אָבִיךָ אֱלֹהֵי אַבְרָהָם וְגוֹ'. נִגְלָה עָלָיו בְּקוֹלוֹ שֶׁל עַמְרָם אָבִיו, כְּדֵי שֶׁלֹּא יִתְיָרֵא...
And he said: “Moses, Moses.” and he said: “Here am I” (Exod. 3:4). ...And He said: I am the God of thy father, the God of Abraham (ibid., v. 6). He appeared to him through the voice of his father, Amram, lest he become frightened...
So what happened? Three siblings get into a fight, the Parent puts on this facade of anger and rebukes them, and then they resolve it. After G-d leaves, Aharon sees Miriam has tzara'at and asks Moshe to pray fro her and she does. We see that the previous friction between the siblings has resolved.
Finally, to understand this more for us, Ramban writes that someone who gets angry, it's like they are experiencing hell. Anger is hell, and hell is anger. One way of understanding hell, is forcing your soul through this constricting, hot, burning process in order for it to be fitting to go into Gan Eden. This is he same thing that happens when we get angry, hot flushed, and our muscles constrict.
תִּתְנַהֵג תָּמִיד לְדַבֵּר כָּל דְּבָרֶיךָ בְּנַחַת, לְכָל אָדָם וּבְכָל עֵת, וּבַזֶּה תִּנָּצֵל מִן הַכַּעַס, שֶׁהִיא מִדָּה רָעָה לְהַחְטִיא בְּנֵי אָדָם. וְכֵן אָמְרוּ רַבּוֹתֵינוּ ז"ל (נדרים כב ע"א): כָּל הַכּוֹעֵס – כָּל מִינֵי גֵיהִנּוֹם שׁוֹלְטִים בּוֹ, שֶׁנֶּאֱמַר (קהלת יא י): "וְהָסֵר כַּעַס מִלִּבֶּךָ, וְהַעֲבֵר רָעָה מִבְּשָׂרֶךָ". וְאֵין "רָעָה" אֶלָּא גֵיהִנּוֹם, שֶׁנֶּאֱמַר (משלי טז ד): "וְגַם רָשָׁע לְיוֹם רָעָה".
When we find ourselves in conflict, when we're angry, we can learn from G-d, to try and bring ourselves to understand the other person's perspective, and bring ourselves to their understanding.
