If this is an InstallShield package, you can create a response file.
Run the installation with the /r switch, and select your installation options as normal. Once installation is complete, you should have a setup.iss file in either c:\windows or c:\windows\system32. Copy this file to the same directory as the installation file.
You can now run the installation file silently using test.exe /s
A lot of .exe installers are "wrapped" installshield or MSIs, that generally expand to a temporary location, and run from there.
Run the installation as normal until it requests some interaction, then look in C:\temp, or wherever your temporary directory is, and it may have expanded itself there.
If it does, then copy the new folder to another location, as they get deleted when the installation completes.
If the contents contain an installshield package, then you can then follow the instructions above. If it contains an MSI, then your best bet would be to create a transform file (MST), and install using the MSI and the MST (not the exe).
As an aside, what is the installation for? If it's an off-the-shelf/downloaded package, the I might be able to give you specific instructions.