It is usually a decent approximation to assume the pre-exponential factor is independent of temperature over small temperature ranges. In that case, you basically have two equations and two unknowns, at which point this is more or less a straightforward algebra problem. You can use whatever method you like to solve it. For Arrhenius problems where the goal is to find the activation energy, the approach of choice is usually to divide one equation by the other, in which case the pre-exponential factor cancels out and you are left with only the activation energy to solve for.