Yeah this may be a late reply, but Yeah the E2 explorers started in 1979. The classic multi-layered timber issue ran into 1980. There apparently was an option of the reverse timber layers too. The second E2s were back to the standard bound bodies and sunburst type finishes. I believe the last of the E2's may have even been metallic paint jobs.
I bought an E2 New in 1981. It was a 1980 manufacture guitar with the multi layered timbers. I paid AUD$1250 (retail AUD$1695) for it and really have not played a guitar since that comes close to it. 27 years later it is still my main weapon of choice.
Check out youtube mindroom666 for a few clips. And to give you an idea of the use I have got from this guitar, the white mark on the scratchplate is actually where I have worn thru the black layer of plastic.
Craig.