How to browse SQL Server Express 2014 Installation directory?

That dialog asks you for the installation media, pay attention. You need to specify the location from where you've run the original install. That is not an Express uninstall, you are uninstalling a licensed SSMS, so you should provide your original, licensed, CDs. To browse for SQL Server installation media

just run the executable (for example: "en_sql_server_2012_express_edition_with_advanced_services_x64.exe")
Navigate to the "options" tab.
Copy the "Installation Media Root Directory" (should look something like the below snipping)
Paste it into the open "Browse for SQL server Installation Media" window.

Remember never uninstall SSMS without taking the entire (local) SQL Server installation out of PC (I don't assume you are acting like this on a server!). Next time, begin with using the SQL Server Installation Center to fix and repair your issues - or dig deeper on the internet before doing anything rash. As to the situation at hand: Per this thread on MSDN, every media holds all versions, it is the license which make the distinguishing. So: Find the installation file (e.g. SQLEXPRADV_x64_ENU.exe) on the machine, and run it! This will take you through the repair/installation process without the need to point to the installation media (which is supposed to be a physical DVD or iso image). If you have deleted the installation file since the first install, just download a new one from Microsoft Download Center.