Let's call the two numbers "x" and "y".
From the problem statement, we know that:
x + y = 38 (equation 1)
x - y = 16 (equation 2)
To solve for x and y, we can use a system of equations.
We can add equation 1 and equation 2 to eliminate y and get:
2x = 54
x = 27
Now we can substitute x = 27 into either equation 1 or equation 2 to solve for y. Let's use equation 1:
x + y = 38
27 + y = 38
y = 11
Therefore, the two numbers are 27 and 11.