1. **State the problem:** We need to find two numbers where the difference between them is 26 and one number is three times the other. 2. **Define variables:** Let the two numbers be $x$ and $y$. 3. **Write the equations based on the problem:** - The difference between the two numbers is 26: $$x - y = 26$$ - One number is three times the other: $$x = 3y$$ 4. **Substitute the second equation into the first:** $$3y - y = 26$$ 5. **Simplify the equation:** $$2y = 26$$ 6. **Solve for $y$:** $$y = \frac{26}{2}$$ $$y = 13$$ 7. **Find $x$ using $x = 3y$:** $$x = 3 \times 13$$ $$x = 39$$ 8. **Answer:** The two numbers are $39$ and $13$.