1. Set up equations:

* Let 'x' be the larger number.

* Let 'y' be the smaller number.

We are given:

* x + y = 21

* x - y = 17

2. Solve for one variable:

* Add the two equations together:

(x + y) + (x - y) = 21 + 17

2x = 38

x = 19

3. Substitute to find the other variable:

* Substitute x = 19 into either of the original equations. Let's use x + y = 21:

19 + y = 21

y = 2

Therefore, the two numbers are 19 and 2.