18 miles on a non-electric bike for a commute sounds punishing.
I did 20 miles round trip commute for a year, before I knew about electric bikes, and it just beat me down so much. It would've been faster, more enjoyable, and safer, had I had an electric bike.
The numbers look solid, I don't think your missing anything from a purely cost perspective.
If the time by car and bike will be the same... go for the bike!