The question is:

A reaction rate doubles when the temperature increases from $25~^\circ\mathrm{C}$ to $40~^\circ\mathrm{C}$. Calculate $E_a$ and the frequency factor.

I found the activation energy to be $35.8~^\circ\mathrm{kJ}$ using the two point form of the Arrhenius equation. What I'm having trouble with is finding the frequency factor. I have two unknowns, $k$ and $A$, and to me it seems like this is impossible to solve without knowing what the rate constant $k$ is. All the examples in the book solves this problem graphically, but apparently you can solve this another way according to my teacher.

The answer given for $A$ is $1.9 \cdot 10^6$ but what method do you use to solve for this?