The difference between two numbers is 10 and their product is 3000. The difference between two numbers is 10
Which would mean x * y = 3000, because "product" is a keyword for "multiplying".
Now we have two equations we can use to obtain the values of x and y, which are: X - y = 10 and x * y = 3000.
Let's take the first equation and solve for x, and then solve for y.
x - y = 10
x = 10 + y
y = x - 10
Now let's plug these in into the multiplication equation. But we need to only plug one variable at a time. Observe:
x * y = 3000
x * (x - 10) = 3000
x^2 - 10x = 3000
x^2 - 10x - 3000 = 0
To solve for x here, we need to use the quadratic formula, which is 
B represents the constant in front of the "x", A stands for the constant in front of the "x^2", and C stands for just the constant without any variable (which would be the -3000).
x = {10 ± √(-10)^2 - 4(1)(-3000)}/2(1)
x = (10 ± √100 + 12000)/2
x = (10 ± √12100)/2
x = (10 ± 110)/2
We have two values for x:
x = (10 + 110)/2 = 120/2 = 60
x = (10 - 110)/2 = -100/2 = -50
Now that we know what x could be, let's plug them back into the original equations.
x = 10 + y
60 = 10 + y
50 = y (Therefore, if x is 60, y must be 50. And it works. Plug these numbers into the equations and they will be equal.)
However, we had a second number for x. Let's plug that in.
x = 10 + y
-50 = 10 + y
-60 = y (If x = -50, then y must be -60. These also work for the original equations when you plug them in, mainly because multiplying two negatives together cancel out the negative signs.)
So you can have: x = 60 and y = 50 OR x = -50 and y = -60.