Merge this into your registry:
Windows Registry Editor Version 5.00 [HKEY_CLASSES_ROOT\.DPR] @="BDS.DprFile" [HKEY_CLASSES_ROOT\BDS.DprFile] @="Delphi Project File" "FriendlyTypeName"=hex(2):40,00,25,00,43,00,6f,00,6d,00,6d,00,6f,00,6e,00,50,\ 00,72,00,6f,00,67,00,72,00,61,00,6d,00,46,00,69,00,6c,00,65,00,73,00,25,00,\ 5c,00,45,00,6d,00,62,00,61,00,72,00,63,00,61,00,64,00,65,00,72,00,6f,00,5c,\ 00,53,00,68,00,65,00,6c,00,6c,00,5c,00,42,00,44,00,53,00,53,00,52,00,2e,00,\ 64,00,6c,00,6c,00,2c,00,2d,00,31,00,37,00,30,00,39,00,00,00 [HKEY_CLASSES_ROOT\BDS.DprFile\DefaultIcon] @="\"C:\\Program Files (x86)\\Embarcadero\\RAD Studio\\10.0\\Bin\\delphicoreide170.bpl\",3" [HKEY_CLASSES_ROOT\BDS.DprFile\Shell] [HKEY_CLASSES_ROOT\BDS.DprFile\Shell\Open] [HKEY_CLASSES_ROOT\BDS.DprFile\Shell\Open\Command] @="\"C:\\Program Files (x86)\\Embarcadero\\RAD Studio\\10.0\\Bin\\bdsLauncher.exe\" \"C:\\Program Files (x86)\\Embarcadero\\RAD Studio\\10.0\\Bin\\bds.exe\" /np" [HKEY_CLASSES_ROOT\BDS.DprFile\Shell\Open\ddeexec] @="[open(\"%1\")]" [HKEY_CLASSES_ROOT\BDS.DprFile\Shell\Open\ddeexec\application] @="bdslauncher" [HKEY_CLASSES_ROOT\BDS.DprFile\Shell\Open\ddeexec\topic] @="system"
Obviously this assumes your XE3 lives in the same place as mine. If it's elsewhere on your machine, then update the paths accordingly.
This is probably easier than an wholesale re-install.