I Need Help Understanding The Type Of Problems That Go Like This; Find Two Numbers Whose Product Is 18 And Whose Sum Is 9?

Usually, the answer to such a problem is a pair of integers. That means you can find the answer by examining the factors of the product value, 18 in this case.
  18 = 1*18 = 2*9 = 3*6
You want the factors whose sum is 9.
  1+18 = 19
  2 + 9 = 11
  3 + 6 = 9
The numbers you seek are 3 and 6.

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The general way to solve a problem like this is to assign a variable to each number and write two equations. Let the numbers be represented by x and y.
  x*y = 18    (two numbers have a product of 18)
  x + y = 9    (the same two numbers have a sum of 9)
We can solve the second equation for y.
  y = 9 - x    (subtract x from both sides of the second equation above)
With this expression for y, we can make a substitution into the first equation.
  x*(9 - x) = 18
This equation can be rearranged into the standard form for quadratics.
  x*9 - x*x = 18    (use the distributive property)
  9x = x^2 + 18    (add x^2 to both sides)
  x^2 - 9x + 18 = 0    (subtract 9x from both sides, swap sides to put the 0 on the right)
This quadratic can be solved several ways. If you don't have a clue about the factors of 18, you can use the quadratic formula. Otherwise you can solve by factoring or by completing the square.
Factoring
  (x - 3)(x - 6) = 0    (this method is essentially equivalent to the one we started with--finding factors of 18 that add to 9)
  x = {3, 6}
Completing the square
  x^2 - 9x + 18 + 2.25 = 2.25    (add a constant so that the constant term on the left is (9/2)^2)
  (x - 4.5)^2 = (1.5)^2    (factor showing the squares)
  x - 4.5 = ±1.5    (square root of both sides)
  x = 4.5 ± 1.5 = {3, 6}    (add 4.5 to both sides and evaluate)
Quadratic formula
  For a*x^2 + b*x + c = 0, the solution is
  x = (-b ±√(b^2 - 4*a*c))/(2*a)
  = (-(-9) ±√((-9)^2 - 4*1*18))/(2*1)
  = (9±√(81-72))/2
  x = (9±3)/2 = {3, 6}
Each of the three methods above yields a value for x. You will note that if x is chosen as one of them, then y = 9-x will be the other one.