I have a site that had all its files erased and there are no backups, but I still have the database. Is it possible to determine which specific version of EE it is, just by looking at the database?
(And no, I was not responsible for backups.)
This would only work if the install of EE had been updated at least once since initial install, but there is a log of version updates found in table exp_update_log. You've probably already checked this, but I thought it might be worth mentioning in case someone else runs into this issue in the future and didn't realize this table existed.
If Steven's answer doesn't get you the version number, you could deduce the general version by the table names and native fields used and comparing them to the ExpressionEngine release notes.
It might not get you to an exact release but perhaps closer than not knowing at all.
(Update: you asked for a "specific version of EE", which my suggestion will not get you.)
potentially, if you restore the db and take a look at exp_sites table and then the site_system_preferences column, decode the encoded content using https://www.base64decode.org and it might just provide the app_version if it was in the config originally.