Presumably, the wrath of the speaker "did end" because he "told" his friend about his anger (line 2). It is the only thing that differentiates the anger he bore against his friend from the anger he bears against his "foe" (3). To his foe, he "told it not" and, instead, kept his anger bottled up inside, giving it the opportunity to grow into something much worse. The speaker gave his friend the opportunity to explain himself, and he opened up the lines of communication, which evidently permitted the situation, and therefore his anger about it, to be resolved. However, the speaker did not give his foe this same chance, and so it had a very different end result. Talking about one's anger with the person with whom one is angry is presented as a much healthier and satisfying choice than harboring it forever.

In "The Poison Tree," the point of the poem is that the anger we hold onto grows into something ugly and poisonous that hurts other people. Blake contrasts this to anger we get over. One good way to overcome anger is to talk about it with the person who angered you. If you can trust another person enough to confide in him and her, you can clear up misunderstandings and give the other person the opportunity to tell his side of the story and explain what happened. It also offers the other person the chance to apologize, because often people don't even know they have offended. With this kind of communication, forgiveness and reconciliation can occur. Then you can move on with your life. In contrast, as the poem shows, if you dwell on your wrath without trying to resolve it, it becomes bigger and bigger and more and more poisonous--Blake imagines it as a poisonous apple--and becomes  especially poisonous if you pretend to the person who offended you that nothing is wrong. 

In the poem "A Poison Tree" by William Blake, why did the speaker's wrath end when he told his friend about it?

In a relationship between friends, there can be disagreement and even anger, certainly, no matter how good the friendship is.  When we value a friendship, we express our disagreement or anger, we talk it out with the friend, and then it is over and done with, we hope. This is in sharp contrast to what the narrator does with his foe, isn't it?  He does not express his anger; he keeps it to himself and nurses it, feeding it, so it grows larger and stronger, ultimately strong enough to poison his foe and kill him. The idea is that when we vent our negative feelings, we are able to be done with them. Those negative feelings we do not express are far more difficult to get over because, the narrator believes, they fester, like an untreated wound. There is disagreement amongst psychologists about this, with some thinking that "getting it all out" is mentally healthy, and others focusing more on changing behavior rather than cathartic release.