a problem needs fast solution

quickcur_at_yahoo.com
Date: 01/22/05 

Date: 21 Jan 2005 17:38:31 -0800

Let:
| 0, if x<1
| a(x-1), if 1<=x<2
| a+b(x-2), if 2<=x<3
f(x)= | a+b+c(x-3), if 3<=x<4
| a+b+c+d(x-4), if 4<=x<5
| a+b+c+d+e(x-5), if 5<=x<6
| a+b+c+d+e+f(x-6), if 6<=x<7
| a+b+c+d+e+f, if 7<=x

| 0, if x<0
| gx, if 0<=x<1
| g+h(x-1), if 1<=x<2
g(x)= | g+h+i(x-2), if 2<=x<3
| g+h+i, if 3<=x<4
| g+h+i(5-x), if 4<=x<5
| g+h(6-x) if 5<=x<6
| g(7-x), if 6<=x<7
| 0 if 7<=x

Now, we have the following equations:
f(x) - f(x - y) = m;
g(x) - g(x - y) = n;

m, n are known. What is the best way to find x, and y?

I want to be fast since I need to find x and y for thousands even
millions of different m, n combinations.

Thanks,

qq