Anger is often a secondary emotion, used to help keep us "safe" from feeling out of control. Often underneath feelings of anger is fear, sadness, jealousy, and other emotions that seem unpleasant to our ego.
The most powerful way that I have found to dissolve anger is to instantly become vulnerable, and speak those feelings that our anger is trying to protect us from. How do we know if we're getting really vulnerable? True, deep vulnerablity leaves us feeling a surge of self-love. When we express those feelings that our ego is trying to mask with anger, our heart becomes vulnerable and opens, and we feel very strong and safe in that moment. In a moment of true vulnerability, it doesn't matter what anyone says to us as a result, because we are empowered with self-love.