Restore DB Backup with limited amount of disk space
SQL Server need to create the database with the size it had when the backup was produced. No way around that.

You can possibly have the backup file on a different machine and restore using an UNC path to that machine. Something like 

RESTORE DATABASE myDB FROM DISK = '\\server\share\db.bak'


Above assumes that the service account for the SQL Server service has permissions on the backup share/file.

But, again, investigate what size each database file had when the backup was produced using RESTORE FILELISTONLY - that is the size the files will be created with.