Technically the logic doesn’t conflict, so yes the plugins can literally be used side by side without any issues.
The voting mechanism this plugin uses actually already exists in Discourse’s code, it’s just not visible. There is a
vote action, and even logic that re-arranges the sort_order property of posts based on number of votes, already in the core Discourse code that is not currently usable in normal Discourse clients. This plugin exposes that action and logic.
The Solved Plugin, by contrast, uses
post_custom_fields to store a boolean value about each post on a topic that can have an accepted answer (if post is accepted = true), and also uses
topic_custom_fields to store the post id of the accepted post (if it exists).
However, there is an open question about what kind of QA system this creates (i.e. a product question). If the OP or an admin can select the solution to a question, then this mitigates the weighting of the ‘crowd-sourced’ method of selecting the answer.
Using them together would create a system a bit like the federal election primaries here in the US. The popular vote for the party’s candidate is mitigated by the votes of the ‘super delegates’ (the OP and the Admins).