Solution - Word Problem

2 sentences contain the information we are after.

The first, [The difference between the 2 numbers is 12], we learn that:

There are 2 numbers we are looking for, as we don't know what they are, we will refer to them as $$x$$ and $$y$$.

The difference of $$x$$ and $$y$$ is 12. This can be mathematically expressed as $$x-y=12$$

From the following sentence, [the product of the 2 numbers is 13], we further learn that the product of $$x$$ and $$y$$ equals 13.

This information, can then be expressed in another equation, which would be $$x\cdot y=13$$

We now have a system of equations:

$$x-y=12$$
$$x\cdot y=13$$