To find two numbers that have a sum of 138 and a difference of 54, we can use a system of equations.
Let x be the larger number and y be the smaller number. Then we have:
x + y = 138 (equation 1)
x - y = 54 (equation 2)
We can solve this system of equations by adding equation 1 and equation 2:
2x = 192
Dividing both sides by 2, we get:
x = 96
Substituting x = 96 into equation 1, we get:
96 + y = 138
Subtracting 96 from both sides, we get:
y = 42
Therefore, the two numbers that have a sum of 138 and a difference of 54 are 96 and 42.