The Impossible Puzzle - CC #2 Mystery Cache
The Impossible Puzzle - CC #2
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Difficulty:
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Terrain:
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Size: 
(micro)
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in our disclaimer.
Cache is NOT at the posted coordinates, those are just suggested parking coordinates.
About the CC series: CC stands for Couch Cache, and it's a series of puzzle caches requiring your brains instead of your body. They're meant to keep you busy during those yucky, rainy, stormy, cold, windy, snowy days, limiting the time you actually need to spend outside. The actual caches are relatively unspectacular micro hides. Solving the puzzle will always directly give you the required cache coordinates.
Paula, Sue and Daisy are mathematical geniuses. They can do any number of calculations in their head instantly. One day, they're given the task of figuring out two numbers. Those two numbers are in the range between 1 and 1000 (inclusive) and they're whole numbers (no decimal numbers). Both numbers can be the same too.
Paula is told the product of both numbers (one number multiplied with the other), Sue is told the sum of both numbers and Daisy is told the difference between the two numbers (one number substracted from the other). However, they're not allowed to tell those numbers to each other.
Then, the following conversation ensues:
Paula: I don't know the two numbers.
Sue: You don't need to tell me that, I've known that already.
Paula: Ah, in that case, I know the numbers now.
Sue: Ok, I know the numbers now too.
Daisy: I still don't know the numbers. I can guess one number, which is likely to be one of the two numbers, but I don't know for sure.
Paula: I know which number you're thinking of, but this one is wrong. It's not one of the two numbers.
Daisy: Ah, then I know the numbers now too.
And that's it! 
Believe it or not, it's actually possible to figure out the two numbers. There's several different approaches to solving this, so I cannot give any hints, as one way may be easier for some people but harder for others, and vice versa.
Write the two numbers as 4 digits (add leading zeroes if necessary) and call the smaller one ABCD and the larger one EFGH. (Example: if the smaller number was 345, A would be 0, B would be 3, C would be 4 and D would be 5.)
N = G*G*G + B*D + C*E*F + (C+A)*G + G
W = C*C*D*H + (B+D)*(E+G) + D - H
Update November 2015: To get the final coordinates, add 26 to N and subtract 73 from W. The geochecker has been updated to reflect this change. You still input the original (old) coordinates into the geochecker and it will tell you the new location (along with a new hint).
Update October 2016: To get the final coordinates, add 53 to N and add 23 to W. The geochecker has been updated to reflect this change. You still input the original (old) coordinates into the geochecker and it will tell you the new location (along with a new hint).
Cache is at: N 43° 28.N' W 80° 32.W'
Good luck!
Congratulations to the first finders:
FTF: Westacular & geocite
2TF: gg7
3TF: Zorkmid
Additional Hints
(No hints available.)