Final answer:
To solve for the numbers J.P. is thinking of, we use the equations x + y = 163 and x - y = 33, which represent their sum and difference respectively.
Step-by-step explanation:
To find the two numbers J.P. is thinking of, we need to set up a system of equations based on the given information that the sum of the numbers is 163, and their difference is 33. Let's denote the two numbers as x and y.
The first equation will represent the sum of the numbers:
1) x + y = 163
The second equation will represent the difference between the numbers:
2) x - y = 33
Using these two equations, we can apply algebraic techniques such as substitution or elimination to solve for x and y. The solution to these equations will give us the two numbers J.P. is thinking of.