The difference of two numbers is 2, and their product is 48. What are the two numbers?

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

From the problem, we have two equations:

1. x - y = 2 (This is given by "the difference of two numbers is 2")

2. xy = 48 (This is given by "their product is 48")

We can solve this system of equations step by step:

Step 1: Solve the first equation for x: x = y + 2

Step 2: Substitute x in the second equation: (y + 2)y = 48

Step 3: This simplifies to y^2 + 2y = 48

Step 4: Rearrange the equation to a standard quadratic form: y^2 + 2y - 48 = 0

Step 5: Factor the quadratic equation: (y - 6)(y + 8) = 0

Step 6: Solve for y: y = 6 or y = -8

Step 7: Substitute y back into the first equation to solve for x:

If y = 6, x = 6 + 2 = 8 If y = -8, x = -8 + 2 = -6

So, the two pairs of numbers that satisfy the conditions are (8, 6) and (-6, -8).