Absolutely, let's solve this problem. Here's how to find the numbers:
**1. Set up the equations:**
* Let 'x' be the first number.
* The second number is 'x + 8' (since it's 8 more than the first).
* The sum of their squares is 80: x² + (x + 8)² = 80
**2. Solve the equation:**
* Expand the equation: x² + x² + 16x + 64 = 80
* Combine like terms: 2x² + 16x - 16 = 0
* Divide by 2 for simplicity: x² + 8x - 8 = 0
* Factor the quadratic equation: (x + 4)(x - 2) = 0
* Solve for possible values of x:
* x + 4 = 0 => x = -4 (We discard this since we need a positive real number)
* x - 2 = 0 => x = 2
**3. Find the second number:**
* Since x = 2, the second number is x + 8 = 2 + 8 = 10
**Answer:** The two numbers are 2 and 10.