Step 1: Let the two numbers be x and y
Step 2: Since we know the difference between the two numbers is 6, that means x = y + 6
Step 3: We also know the sum of the two numbers is 10, so x + y + 6 = 10
Step 4: Simplifying, we get 2y + 6 = 10
Step 5: Subtracting 6 from both sides, we get 2y = 4
Step 6: Dividing both sides by 2, we get y = 2
Step 7: Finally, we can use the first equation (x = y + 6) to solve for x, so x = 8
Therefore, the two numbers are 8 and 2.