Determining SQL Server Server Edition without database access
If you have access to file system, one way of getting information could be to check available folders under %PROGRAMFILES%\Microsoft SQL Server\xyz

where xyz translates to:


 80 = SQL Server 2000    =  8.00.xxxx
 90 = SQL Server 2005    =  9.00.xxxx
100 = SQL Server 2008    = 10.00.xxxx
105 = SQL Server 2008 R2 = 10.50.xxxx
110 = SQL Server 2012    = 11.00.xxxx
120 = SQL Server 2014    = 12.00.xxxx
130 = SQL Server 2016    = 13.00.xxxx


Further you can analyze the installation summary file located at
%PROGRAMFILES%\Microsoft SQL Server\xyz\Setup Bootstrap\Log\Summary.txt
which will give you package properties that contains information about Installation edition (Enterprise).