Hi and welcome.
The only 360 Yamaha list is a DT360 which is a trials (dirt) style bike and the 'E' probably refers to electronic ignition. If it's not a dirt bike try and get some pictures and post them on here and see if anyone can shed some light.
Incidentally if it's any help with your cause no major manufacturer puts an 'experimental' bike on the road, they need to go through so many stringent type approval tests it wouldn't be worth their while just for a production run of a couple of hundred bikes. If it was a small builder then maybe, but Yamaha are one of the biggest in the world and the set-up costs would be prohibitively expensive.