Is getting angry a biblical prohibition? If so, what is the source in the Torah (five books of Moses) prohibiting getting angry (preferably something explicit)?
R. Simeon b. Eleazar said in the name of Halfa b. Agra in R. Johanan b. Nuri's name: He who rends his garments in his anger, he who breaks his vessels in his anger, and he who scatters his money in his anger, regard him as an idolater, because such are the wiles of the Tempter: To-day he says to him, 'Do this'; to-morrow he tells him, 'Do that,' until he bids him, 'Go and serve idols,' and he goes and serves [them]. R. Abin observed: What verse [intimates this]? There shall be no strange god in thee; neither shalt thou worship any strange god; who is the strange god that resides in man himself? Say, that is the Tempter!
We see that the Talmud likens anger to idolatry, a biblical prohibition. The object of worship in this case is the self; the Evil Inclination, hinted at as a strange god residing within man by Psalms 81:10
Another different answer:
Ohr Somayach answered a question on anger and said:
Anger is considered one of the most destructive traits. Yaakov Avinu (Jacob) strongly admonishes his children Shimon and Levi "Accursed is their rage for it is intense, and their wrath for it is harsh..." Genesis 49:6-7.
So we found that our forefather Yaakov condemned the rage and anger of Shimon and Levi. Ohr Someach goes on to say:
It is puzzling that "anger" is so destructive and is nevertheless not the subject of a direct commandment. There is no mitzvah "Thou shalt not be angry." Rav Chaim Vital in his classic work "Sha'arei Kedusha" addresses this question, and answers it with a very profound concept. Before we ever get to the point of performing mitzvot there is a need to develop our basic character. The traits that comprise our character determine the way in which we fulfill the mitzvot. We must spend our energy in perfecting these aspects of ourselves - once these are properly developed we can perform the mitzvot with relative ease.
Conclusion: Overcoming anger is a foundation for the proper fulfillment of the entire Torah, and is therefore not counted as a separate mitzvah.
In Iggeres Haramban, one of the main points the Ramban is trying to get over to his son is not to get angry. While the Torah does not say that being angry is prohibited, it is a very bad trait. Here is some of what the Ramban writes:
Get into the habit of always speaking calmly to everyone. This will prevent you from anger, a serious character flaw which causes people to sin. As our Rabbis said (Nedarim 22a): Whoever flares up in anger is subject to the discipline of Gehinnom as it is says in (Koheles 12:10), "Cast out anger from your heart, and [by doing this] remove evil from your flesh." "Evil" here means Gehinnom, as we read (Mishlei 16:4): "...and the wicked are destined for the day of evil."
Shmos 35:3 prohibits lighting fires on Shabbat: “Do not kindle a fire in any of your residences on the day of Shabbat.”
Daily Halacha.com relates this “fire” to anger.
The question is asked why did Moshe make particular mention of the prohibition against kindling a fire?
One of the answers that have been suggested is that Moshe actually refers here to the “fire” of anger. He warns us in this Pasuk of the need to avoid anger on Shabbat.
Shabbat thus offers us the opportunity for spiritual greatness, but also poses the risk of spiritual destruction by putting people close together and making them prone to anger. An even greater threat, though, arises in the hours before Shabbat, on Friday afternoon. Especially in the winter months, when Shabbat begins early Friday afternoon, these hours are a very tense and pressured time. There’s a lot to get done, and people are anxious. And, while I have not conducted a scientific survey on the subject, I would venture to guess that the majority of household problems happen to take place on Friday. It seems like it’s always Friday when the shirt is missing a button or the oven breaks. If we took a survey of community plumbers, I imagine we would hear of a disproportionately large number of leaks, bursts and boiler breakdowns specifically on Fridays. This is the Satan trying to interfere with the beauty and spiritual benefits of Shabbat. He finds ways to get people nervous and agitated which in turn causes them to become angry and shout at one another, so that the family sits down at the table upset, aggravated, and not at all interested in sharing a beautiful Shabbat experience together.
So there is at least an interpretation of a possuk which prohibits anger on Shabbat and around Shabbat. It is not explicit in the possuk and does not cover other days of the week.
Torah is also reflected in unchanging laws of nature. When angry (especially prolonged), real stress, lowers your immune system, disrupts learning and concentration, distracts, and breeds other negative vibes to others. It effects performance of his job, as well as learning.
Since we are not allowed to harm abuse ourselves, even so we are not allowed to cause harm to others. This is why Ahavath Yisrael is so important.
Disappointed would probably be a better way to channel anger away. It is all in the mind. And when the mind is occupied in Torah, then there is no room for negative inspiration.