1. **State the problem:** We are given that the sum of two numbers is 40 and their difference is 8. We need to find the two numbers. 2. **Set variables:** Let the larger number be $x$ and the smaller number be $y$. 3. **Write equations:** From the problem, we have two equations: $$x + y = 40$$ $$x - y = 8$$ 4. **Add the equations:** Adding both equations to eliminate $y$: $$ (x + y) + (x - y) = 40 + 8 $$ $$ 2x = 48 $$ 5. **Solve for $x$:** $$ x = \frac{48}{2} = 24 $$ 6. **Substitute $x$ back to find $y$:** Using $x + y = 40$: $$ 24 + y = 40 $$ $$ y = 40 - 24 = 16 $$ 7. **Answer:** The larger number is $24$ and the smaller number is $16$. This method uses the system of linear equations and the elimination technique to find the values of the two numbers.