Can I e-file my unfiled 2018 taxes without having to mail them in? If I receive a return from 2019 taxes how can I use that to cover 2018 back taxes? EFTPS applied for.

Unfortunately, you cannot e-file prior year returns.  The IRS only allows e-files for the current tax year.  You will need to mail them.

If the IRS knows you have a balance due on your 2018 return, they will automatically apply your refund (or part of your refund to that year).  However, late filed 2018 returns will not have a priority of being processed during the IRS busy season.  It may take several months for a prior year return to be processed.