There is no such thing as far as I know. The RE refers to a re-entry permit obtained to keep a Non O permission to stay "alive" when you leave Thailand during that period you are stamped in for.
Since my first visit to Thailand in 1996, on Visa Exempt, Tourist Visas and lately Non O based on marriage, averaging 3 visits a year, I have NEVER been asked for an onward or return ticket by an Immigration Officer. It has been a different story at check-in at Glasgow, all visits over 30 days have been queried by the staff. KLM were once on the verge of refusing me on a Visa Exempt, saying you can't stay 31 days, until I pointed out that I didn't get there until tomorrow !
If it was an official marriage ceremony at the district office, you can get a Non Immigrant O Visa based on that marriage which gives you a 90 day permission to stay.