I think this is a zero sum problem. It can't be a functions problem. Just sheer logic. Otherwise, it would take forever. It seems that each column could easily add up to zero, which would mean that all numbers would be zero.
Edit: Zippy: Yes, I think so, good show.
Further edit: Of course, no number is supposed to be repeated according to our leader!
Further, further edit: On the other hand, Thirty should add up to 30 and ninety to 90, so all zeroes is not possible. My bad.