To solve this problem, I need to find the two numbers first. I can use a system of equations to represent the given information: x + y = 40 and x - y = 12. I can add the two equations together to eliminate y and get 2x = 52. Dividing both sides by 2, I get x = 26. Now that I have x, I can plug it into either equation to get y. I'll use the first one: 26 + y = 40. Subtracting 26 from both sides, I get y = 14. So the two numbers are 26 and 14. To find their product, I just need to multiply them together: 26 * 14 = 364. 
The sum of two numbers is 40 and their difference is 12. What is their product?