1. The problem asks us to show that the difference between $3^2$ and $3^3$ is 18. 2. Calculate $3^2$: $$3^2 = 3 \times 3 = 9$$ 3. Calculate $3^3$: $$3^3 = 3 \times 3 \times 3 = 27$$ 4. Find the difference between $3^3$ and $3^2$: $$3^3 - 3^2 = 27 - 9 = 18$$ 5. Therefore, the difference between $3^2$ and $3^3$ is indeed 18, as required.