No W-2

You don’t need a W_2 to file. Report what you have. 

What form do I use to report what I have? The 1040 has no place to report all the info from both forms.

It appears that I can only report Form 1098-E with TurboTax

I then have to fill out form 8962 to submit separately, assume through snail mail, with the 1095-A that was sent to me. 

You may not need to file. Take this quick quiz, Filing requirement - Do I need to file a tax return? 

Note that you have to file if you have 1095-A with advanced premium credits in column C.