Is there such a way to adapt E-mount lenses to A-mount bodies? If not is there a reason this can not be done? If there is such an adapter can you recommend an adapter to me?
No, it works the other way around. The main measure to know is the flange distance. This is the distance between the mount and sensor on a camera. Lenses for a particular mount are designed for exactly that distance. If a lens would be mounted with the wrong flange distance it would not be able to achieve focus for more than a very short distance, usually a few inches from the lens.
You can adapt a lens made for a longer flange distance to a mount with a shorter one. This is mostly done by filling the gap with a light-proof tube. Modern such adapters also forward electric contacts and sometimes mechanical connections.
Mirrorless cameras are designed with short flange distances and DSLRs longer ones to allow for the mirror to swing during operation. For this reason, there is A-mount lens to E-mount adapter, a Four-Thirds lens to Micro Four-Thirds and an EF-S to EF-M but not the other way around. At least those pairs of mounts were designed to be compatible which lets most lenses work normally.