Let's call the two numbers we're trying to find x and y. We know that x + y = 12 and xy = 23. From the first equation, we can solve for one of the variables in terms of the other. So if we subtract x from both sides, we get y = 12 - x. Now we can substitute this expression for y into the second equation to get x(12 - x) = 23. Expanding this out, we get 12x - x^2 = 23. Rearranging, we get x^2 - 12x + 23 = 0. This quadratic equation can be factored as (x - 2)(x - 10) = 0. So either x = 2 and y = 10, or x = 10 and y = 2.