Came across this thread when having the same problem as OP. Wanted to share my variation of the solution presented by "crazysuperjeff". FYI, I'm running Linux Mint 19.
When trying these commands, directly, as-is...
$ wget -qO - https://download.sublimetext.com/sublimehq-pub.gpg
$ sudo apt-key add sublimehq-pub.gpg
The key would "download" (i.e. it would be shown in my terminal) but when I tried the 2nd command to add it, I would get this error:
"gpg: can't open 'sublimehq-pub.gpg': No such file or directory"
So what did work for me, was the click on the link for the .gpg file itself (https://download.sublimetext.com/sublimehq-pub.gpg), save the file to wherever (downloads, desktop, etc), then 'cd' into that directory and run the 2nd command.
Once I did that, I got the OK message from my terminal.