Here is an easy explanation.
Confirm. The correct known answer already exists. You just need to confirm that your solution yields that same (correct) answer. Think about it as checking your answer in a workbook- did you get the same answer that is listed in the back of the book?
Verify. The solution has to be reworked to verify your answer is correct. Think of this as double-checking your work. You correctly work through the steps of the solution a second time. Did your first answer match what you got when correctly working through the problem a second time?
Based on the most up-voted answer, it almost seems as if one could conclude that "confirmation" would not require external evidence. But, that isn't quite the case. The confirmation itself is held to the assertion that it is backed by evidence, if it assumed to be true.