1. **State the problem:** We are given two numbers whose sum is 18 and their difference is 4. We need to find the larger number. 2. **Set variables:** Let the two numbers be $x$ and $y$, where $x$ is the larger number and $y$ is the smaller number. 3. **Write equations:** From the problem, we have: $$x + y = 18$$ $$x - y = 4$$ 4. **Add the two equations:** Adding both equations eliminates $y$: $$ (x + y) + (x - y) = 18 + 4 $$ $$ 2x = 22 $$ 5. **Solve for $x$:** $$ x = \frac{22}{2} = 11 $$ 6. **Interpretation:** The larger number is $11$. 7. **Check:** The smaller number $y = 18 - x = 18 - 11 = 7$. The difference $11 - 7 = 4$ matches the problem statement. **Final answer:** The larger number is $11$.