Okay, so you know the temperature, gas constant and activation energy (and we're making the assumption that Ea and A don't change with temperature, which is wrong, but that doesn't matter) for two values of k.
k = Ae^-Ea/RT
OR
ln(k) = ln(A)-Ea/R(1/T)
Pick your poison and fill this equation in for both rate constants, then just divide one by the other.
Substitute the known value of k in for k1 or whatever you want to call it.
k2
Ae^-108x10^3/ 8.314 x 310
__________ ________________________
1.85 x 10^-4 =
Ae^-108x10^3 / 8.314 x 298
k2 = 1.85 x 10^-4 * 5.406 (that's the value I got for the fraction on the right, I could have made a calculator error :s)
= 1.00 x 10^-3
I didn't include units but you should probably work those out on the side using the same fractions

Is that the right answer???