>I didn't download msi package. I downloaded SQLEXPR_x64_ENU.EXE which is probably SQL Server without tools. So now I don't want to uninstall the SQL Server but find a SSMS separately and install it.

Right, that exe didn't have SSMS and you're right, you should be able to download and install SSMS separately. I would go with the latest SSMS you can find.