I see Kitsur Shulchan aruch 29.4,13 Regarding anger and hatred.
What is the difference?
Is anger the expression of hatred?
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They both arise from the same branch, namely arrogance.
in Shaarei Kedusha part 1 gate 2:
The foundation of Fire - from it is drawn arrogance which is called "Gasut HaRuach" - in being the lightest and highest of all the foundations. And included in it is anger, since it is because of arrogance that a man becomes angry when "his will is not being done". And if he were a "shefal ruach" (lowly of spirit), and he recognized his lacking, he would not at all become angry. It comes out that anger and arrogance are one trait. And their derivatives are 3: kapdanus (being irritable) in his heart. Because without the arrogance, he would not be irritable in his heart, similar to what we explained for anger. Seeking power and honor to show off to others. Hatred of others because they are greater than him. And this is also a branch of arrogance. (Translation my own).