"The Perfect Logicians" Puzzle

Puzzles of any kind (mathematical, logic etc) is certainly a way to kill some time. It also can be a very efficient and clear way to test your abilities in dealing with complex situations and developing the proper solutions.

Personally I have often found myself derailing from my everyday routine, struggling to solve such problems. My favorites are the kind where the problem is easily stated (some lines), resists hard to usual thinking but surrenders easily to a different but also ingenious approach.
Enjoy!

The problem can be stated as follows.

We have two integers, say α and β, for which it is known that

β>α>1 and α+β<100

There are two perfect logicians, say P and S.
P is given the product of the numbers and S is given the sum of them.
P calls S on the phone and a short conversation follows:

P: I cannot find the numbers...
S: I knew that.
P: Hmm..Now I can!
S: Well, now I can find them too!

Can you find the numbers?
(Use of computer programming is advised!)


You can find a solution to the perfect logicians puzzle here.