1. **State the problem:** Two numbers have a sum of 18, and one number is 6 more than the other. 2. **Write the simultaneous equations:** Let the two numbers be $x$ and $y$. - The sum is 18: $$x + y = 18$$ - One number is 6 more than the other: $$x = y + 6$$ 3. **Substitute and solve:** Substitute $x = y + 6$ into the first equation: $$ (y + 6) + y = 18 $$ 4. **Simplify:** $$ y + 6 + y = 18 $$ $$ 2y + 6 = 18 $$ 5. **Isolate $y$:** $$ 2y + 6 = 18 $$ $$ 2y = 18 - 6 $$ $$ 2y = 12 $$ 6. **Divide both sides by 2:** $$ \cancel{2}y = \cancel{2}6 $$ $$ y = 6 $$ 7. **Find $x$ using $x = y + 6$:** $$ x = 6 + 6 $$ $$ x = 12 $$ **Final answer:** The two numbers are $12$ and $6$.