NORTH + WEST = CACHE
Each letter represents a different numeral from 0 to 9.
Neither N, W nor C is 0
The Cache can be found at
N 51 X
W 000 Y
where X and Y are 4 or 5 digit numbers given by,
X = H * E * OSTW
Y = E * S * NRC
for example if X = 23,456, then the Northing would be N 51 23.456
There are 6 solutions, though some you will be able to rule out. The solution I have used is the one which gives a final location closest to the given coordinates.
I worked out the solution that I based the puzzle on by hand, though I'm not sure whether there is purely logical method to derive all solutions. Brute force seems a popular method amongst solvers. I'll try and see if I can come up with another cache puzzle that is soluble by logic alone.