Let's denote the two numbers as $x$ and $y$.

We know two things:

1. The sum of the two numbers is 67: $x + y = 67$
2. The difference between the two numbers is 13: $x - y = 13$

To solve for $x$ and $y$, we can add and subtract these equations:

Step 1: Add the two equations.

$(x + y) + (x - y) = 67 + 13$ This simplifies to: $2x = 80$ So: $x = 40$

Step 2: Substitute $x = 40$ back into the sum equation.

$40 + y = 67$ This simplifies to: $y = 27$

Conclusion:

The two numbers are 40 and 27.

Would you like more details or have any questions?

Here are five related questions:

1. What is the product of the two numbers?
2. If the sum was 80 and the difference was 20, what would the two numbers be?
3. How would the problem change if the difference was negative?
4. Can you express one number in terms of the other?
5. What if you had three numbers with a specific sum and two different differences?

Tip: When working with equations involving sums and differences, adding and subtracting equations is a powerful technique for isolating variables.