Answer:
43 and 5
Step-by-step explanation:
Let's let the two unknown numbers be a and b.
Their sum is 48, therefore:

And their difference is 38. In other words:

We now have a system of equations. To solve, we can use substitution. First, add b to both sides in the second equation:

Substitute this into the first equation:

Combine like terms:

Subtract 38 from both sides:

Divide both sides by 2:

So, one of the numbers is 5.
The sum of them is 48. Therefore, the other number is 48-5 or 43.
So, our two numbers are 43 and 5.
And we're done!