Is there a word for opposite numbers?

It's called the additive inverse.

In a less technical context, you could just call them negatives of each other.

Similarly, 5 and 1/5 are multiplicative inverses.

This is hardly mainstream English, but there is a term.

The identity element under addition for the set of reals (or the set of integers) is zero;

x + 0 = 0 + x = x

The element that must be added to any element to give the identity element as the product (the general term for result of a binary operation; here the sum) is, for addition, known as the additive inverse of that element (number).

As noted by Barmar, additive inverse is the technically correct term, but in your context, you could use the following phrase:

There's an issue with records that contain values that differ only in their sign. For example, -100 and +100.

You could also say:

There's an issue with records that contain values that have equal magnitude but opposite sign. For example, -100 and +100.

I have read both these in various textbooks written by American authors. You could pick one of these alternatives, or a similar variant, depending on your audience.