Let's solve this problem step by step.

Let the two numbers be $x$ and $y$. According to the problem:

1. The sum of the two numbers is 39: $x + y = 39$

2. One number is 2 times as large as the other: $x = 2y$

Now, substitute the expression for $x$ from the second equation into the first equation:

$2y + y = 39$

Combine like terms:

$3y = 39$

Solve for $y$:

$y = \frac{39}{3} = 13$

Now that we have $y = 13$, substitute this value back into the equation $x = 2y$:

$x = 2 \times 13 = 26$

So, the two numbers are $x = 26$ and $y = 13$.

Would you like more details or have any questions?

Here are 8 related questions to explore:

1. What if the sum of the two numbers was 50 instead of 39?
2. How would the solution change if one number was 3 times as large as the other?
3. Can you solve for the two numbers if their difference is given instead of their sum?
4. What if the relationship was $x = \frac{1}{2}y$ instead of $x = 2y$?
5. How do you solve this problem using a system of equations?
6. What are the properties of the numbers if the sum is a negative number?
7. How does the problem change if both numbers are negative?
8. Can you solve the problem using graphical methods?

Tip: When dealing with problems involving multiple conditions, try expressing one variable in terms of the other to simplify the problem.