Ramanujan's Secrets

$\phi(q) = \prod_{k=1}^{\infty}(1-q^k)$ The above function is also called, Euler's function. If the value of $\phi(e^{-8\pi})$ can be written as: $\large \dfrac{e^{\frac{\pi}{A}}\Gamma\left(\dfrac{1}{B}\right)}{E^{\frac{C}{D}}\pi^{\frac{A}{B}}}(\sqrt{E}-1)^{1/B}$ where $A,B,C,D,E$ are positive integers, with $\gcd(C,D)=1, \gcd(A,B)=1$ and $E$ being square free, submit the value of $A+B+C+D+E$