1. **Problem:** The sum of two numbers is 35. One number is 7 more than the other. Find the two numbers. 2. **Step 1: Define variables.** Let the first number be $x$. Then the second number is $x + 7$ because it is 7 more than the first. 3. **Step 2: Write the equation for the sum.** The sum of the two numbers is 35, so: $$x + (x + 7) = 35$$ 4. **Step 3: Simplify the equation.** $$2x + 7 = 35$$ 5. **Step 4: Solve for $x$.** Subtract 7 from both sides: $$2x + \cancel{7} - \cancel{7} = 35 - 7$$ $$2x = 28$$ 6. **Step 5: Divide both sides by 2 to isolate $x$.** $$\frac{2x}{\cancel{2}} = \frac{28}{\cancel{2}}$$ $$x = 14$$ 7. **Step 6: Find the second number.** $$x + 7 = 14 + 7 = 21$$ 8. **Answer:** The two numbers are $14$ and $21$.