According to the Arrhenius equation, the relationship between the rate constant and temperature is given by: $\log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right]$ where $k_1$ and $k_2$ are the rate constants at temperatures $T_1$ and $T_2$ respectively, $E_a$ is the activation energy, and $R$ is the gas constant. Thus, if the rate constants at two different temperatures are known, the activation energy of the reaction can be easily calculated.