So for this, we will be doing a system of equations, one equation representing the sum and the other representing the difference. Let x = larger number and y = smaller number:

For this, I will be using the elimination method. With these equations, add them together to get
. From here we can solve for x.
For this, just divide both sides by 2 and your first answer is

Now that we have the value of x, substitute it into either equation to solve for y:

In short, the two numbers are 12 and 7.