1. **State the problem:** We are given two numbers whose sum is 36, and one number exceeds the other by 8. We need to find the smaller number. 2. **Set variables:** Let the smaller number be $x$. Then the larger number is $x + 8$. 3. **Write the equation for the sum:** According to the problem, the sum of the two numbers is 36, so: $$x + (x + 8) = 36$$ 4. **Simplify the equation:** $$2x + 8 = 36$$ 5. **Solve for $x$:** Subtract 8 from both sides: $$2x = 36 - 8$$ $$2x = 28$$ Divide both sides by 2: $$x = \frac{28}{2} = 14$$ 6. **Conclusion:** The smaller number is $14$.