You could point to another page or the same one. I think with the "add two numbers" example you describe I'd probably use one page and use the input form data to initialize the input text fields (or leave them blank if the input isn't set, like the first time you go to the page), and then check to see if both input variables are set to numbers, and if so display the answer.
As far as GET vs POST, both with will work. I had never really thought about it much until you asked, so I searched and found this answer:
http://stackoverflow.com/questions/4...do-you-use-get