It would be nice to get a bit more context. Before I read the other answers, I actually thought hard sums might refer to concrete or verified calculations, as in cold, hard facts, or hard numbers. If these hard sums are sums of money, for example, then we can talk about hard dollars (in the U.S.), which are objectively quantifiable sums (like the number of dollars it would cost to buy a new computer system); versus soft dollars, which are not so objectively quantifiable (like the value of productivity losses or low morale endured while switching to the new computer system).
Edit: Now that I've got the context, I see that my answer doesn't apply. Please see the other responses that have to do with "difficult arithmetic".