1. Stating the problem: Find two numbers $x$ and $y$ such that their sum is 12 and their difference is 4. 2. Write equations from the problem: $$x + y = 12$$ $$x - y = 4$$ 3. Add the two equations to eliminate $y$: $$(x + y) + (x - y) = 12 + 4$$ $$2x = 16$$ 4. Solve for $x$: $$x = \frac{16}{2} = 8$$ 5. Substitute $x = 8$ into one of the original equations, for example $x + y = 12$: $$8 + y = 12$$ 6. Solve for $y$: $$y = 12 - 8 = 4$$ 7. Final answer: The two numbers are $8$ and $4$.