In Mishlei, it is written, מענה רך משיב חמה, a gentle response conquers anger. Shlomo Hamelech is telling us the importance of not raising our voices in any conversation. This is seconded by the Ramban in אגרת הרמב”ן, when he refers to this gentle response as דיבור בנחת.
Rabbeinu Bechaye felt that this was the key to Yehuda’s handling of Yosef. He did not allow himself to lose his cool, even though he was very annoyed with Yosef.
Anger, or כעס, can be one of the most harmful negative character traits that one can have.
The Ramban says it very succinctly in his letter to his son. Conquer anger and you achieve humility, ענווה. When you have humility, it opens the door to all of the good things in life; and the most important one is the closeness to Hashem that comes with humility.