OK, spelling this out for the benefit of others who may have the same puzzle.
1. Suppose you post a topic-starting message that contains an actual solution already. There's no facility to mark that as a solution.
2. You can reply to that post with a dummy message. (While creating that reply, there's no facility to mark it as a solution.) Post that message.
3. In the list of messages for that topic, find the just-posted message. Since it's a reply, it has both Reply and "Accept as Solution" buttons. Hit the "Accept..." button.
Bottom line: The "Solved" feature is oriented to the use-case of people asking a question, then someone else providing the solution message, then the original poster accepting that message as a solution. As a side-effect of having an accepted message, the topic/thread gains a "Solved" status.