Product and Sum puzzle

This is being my favorite pass-time I was searching for some maths puzzle and found this one which turned out to be the toughest I ever came across.

Let x and y be two integers with 1 < x < y and x+y <= 100. Suppose Ms S is given the value of x+y and Mr P is given the value of x*y. 1.Mr P says: "I don't know the values of x and y." 2.Ms S replies: "I knew that you didn't know the values." 3.Mr P responds: "Oh, then I do know the values of x and y." 4.Ms S exclaims: "Oh, then so do I." What are the values of x and y? This has unique solutions. For solutions please visit Dijkstra's Paper