I'm assuming that you would like to remain with your current firm if "the price was right", or you probably wouldn't be asking this question.
I believe you could approach your boss politely and tactfully - you don't have to just go and look for another job. Since he offered you a full time position he apparently values your work, but may be trying to "lowball you" as the opening move in negotiations. That's not necessarily something you should hold against him - it's just business. (Similarly, your desire to earn more than what he's offering isn't "greedy" - you deserve appropriate compensation for your work.) You already have more knowledge about your boss than just that offer, since you've worked there for a time, and with my suggestion you'll learn even more:
When I did the math based on current market average for engineers with
no experience in my specialty and geographic location, accounting for
taxes, and if I buy my own health insurance/dental/optical, then I
stand to lose $18k per year.
Your math, or what it says in some survey, may not be enough to get him to offer you more. I know it wouldn't convince me - I'd simply say "Go see if you can find a job like that". If I was in your position, I would ask the boss for a weeks or two to think about it, and "go shopping" - test the actual market waters and see if you can get an offer that you believe is appropriate. Then you can go back to your current boss and say "I like working here and I think I can make a good contribution, but I have an offer of $X with benefits (etc) - might you be willing to agree to such terms...?" If you're lucky, he will agree and maybe even up the ante. If not, he'll tell you he's not interested, and you'll know what to do.
If your boss refuses to give you time to consider - "take it or leave it" - I'd consider this a red flag: He probably knows he's low-balling you and is trying to pressure you into a bad deal before you have a chance to consider your options.