physical chemistry - Application of the Arrhenius equation to a parallel reaction

I'm struggling with this homework question: "For a parallel reaction A goes to B with rate constant $k_1$ and A goes to C with rate constant $k_2$, you determine that the activation energies are 71.9 kJ/mol for $k_1$ and 142.8 kJ/mol for $k_2$. If the rate constants are equal at a temperature of 321 K, at what temperature (in K) will $\frac{k_1}{k_2} = 2$?"

I know I have to use $k=Ae^{\frac{E}{RT}}$, and I've tried solving for $T$ after filling in my data into the formula as ratios, ie $\frac{k_1}{k_2}$, $\frac{E_1}{E_2}$, etc, but I can't seem to get a coherent answer.

I tried $\ln\frac{k_1}{k_2})=-\frac{E}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$ as well, but in that case I don't know what $E$ I'm supposed to use.

Any guidance on figuring this out would be much appreciated.