Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and
x+y < 100. S is given the value x+y and P is given the value xy. They then have the following conversation.
P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.
Given that the above statements are true, what are the two numbers?
Answers are expected as comments.