1. **Problem:** Difference of two numbers is 18 and their ratio is 10. Find the numbers. 2. **Step 1: Define variables.** Let the two numbers be $x$ and $y$ such that $x > y$. 3. **Step 2: Write the given conditions as equations.** - Difference: $$x - y = 18$$ - Ratio: $$\frac{x}{y} = 10$$ 4. **Step 3: Express $x$ in terms of $y$ using the ratio.** $$x = 10y$$ 5. **Step 4: Substitute $x$ in the difference equation.** $$10y - y = 18$$ $$9y = 18$$ 6. **Step 5: Solve for $y$.** $$y = \frac{18}{9} = 2$$ 7. **Step 6: Find $x$ using $x = 10y$.** $$x = 10 \times 2 = 20$$ 8. **Answer:** The two numbers are $20$ and $2$. These satisfy both the difference and ratio conditions.