I have reached 1800 online on another site just by playing a lot of games. I also like to look through master games, but I don't really study them heavily.
When I started online on that site, I got a provisional rating of around 1550, it only took me about 6 months get to 1830.
It is definitely possible, and shouldn't be too hard if you really want to commit yourself to it. Just attack the problem from as many angles as possible.
Chess.com is a perfect learning place with endless learning sources. But can one have 1800+ with these sources without a personal coach?