what's the difference between 返事 and 答え？

Question

both have the similar English of "answer," but when do you use one over the other?

Answer 1

From goo both 答え and 返事 can have the meaning of "呼びかけに対して答える言葉", which is what "answer" or "response" is used for in English.

But 答え has another meaning "問題・設問などを解いて出される結果", which what I would summarize as equivalent to "solution", while 返事 has "返答の手紙", which is equivalent to "reply".

I guess I could say that 答え is answer to a call/address or a question, while 返事 is answer to a call/address or a letter. Or put it another way, you can use 答え or 返事 interchangeably when referring to answering a call/address but for a solution to a question or problem 答え should be use, and for answering a letter 返事 should be used.