Hi,
does this work for you?
(*Generate data*)
x = RandomReal[1, {100}]; y = RandomReal[1, {100}];
(*Interpolate*)
f = Interpolation[x]; g = Interpolation[y];
(*Define difference function*)
h = f[#] - g[#] &
(*Evaluate h*)
h[5]
(*Out:= -0.193709*)
(*Plot h*)
Plot[h[x],{x,1,100}]
If you are careful about it, you can even differentiate it (I used InterpolationOrder-> 2 for this):
Plot[h'[b], {b, 1, 100}]
Cheers,
Marco
