OK I'm back. 

Alfred would have known his isn't 10, because if it were and so were batman's, then Robin would be able to deduce his is 20. This is because he sees 10 and 10. He knows 20-10=10 is not valid because Riddler wants only positive numbers.
If Batman is 10, then Alfred knows his number. 
Batman is 50

Fiatrevelation

 accurate of an explanation.  Riddler didn't say that the three integers had to be unique.

science

[Logic Puzzle] The Riddler's Challenge

SimpleStacker

Oooh, this is very close, but it's not *quite* accurate of an explanation.  Riddler didn't say that the three integers had to be unique.