The sum and difference of two numbers are 19 and 7, respectively. What is the…

Let the two numbers be x and y.

We are given the system: x + y = 19 and x - y = 7.

Adding the equations yields 2x = 26, so x = 13.

Substituting x = 13 into the first equation gives y = 6.

The sum of their squares is 13² + 6² = 169 + 36 = 205.