1. **State the problem:** We are given two numbers whose sum is 9067 and their difference is 6523. We need to find the smaller 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 the equations:** $$x + y = 9067$$ $$x - y = 6523$$ 4. **Add the two equations to eliminate $y$:** $$ (x + y) + (x - y) = 9067 + 6523 $$ $$ 2x = 15590 $$ 5. **Solve for $x$:** $$ x = \frac{15590}{2} $$ $$ x = 7795 $$ 6. **Substitute $x$ back into the sum equation to find $y$:** $$ 7795 + y = 9067 $$ $$ y = 9067 - 7795 $$ $$ y = 1272 $$ 7. **Answer:** The smaller number is $\boxed{1272}$.