Choice C is the correct answer. Let $x$ be the larger number and $y$ be the smaller number.

System: $\begin{cases} x + y = 36 \\ x - y = 10 \end{cases}$

Step 1: Add the equations to eliminate $y$: $2x = 46$$x = 23$

Step 2: Find $y$ using $x + y = 36$: $23 + y = 36$$y = 13$

Solution: The larger number is 23.

Verification: $23 + 13 = 36$ ✓ and $23 - 13 = 10$ ✓

💡 Strategic Tip: Addition is perfect for sum-and-difference problems.

Choice A is incorrect because$20 + 16 = 36$ ✓, but $20 - 16 = 4 \ eq 10$.

Choice B is incorrect because$24 + 12 = 36$ ✓, but $24 - 12 = 12 \ eq 10$.

Choice D is incorrect because$26 + 10 = 36$ ✓, but $26 - 10 = 16 \ eq 10$.