p.
but before you go ahead, check what time machine is actually backing up. Not unheard of for people to do this and then remember that they had excluded their apps folder or some other useful folder from their TM backups. If you are doing this then go to the TM prefs in system prefs and remove any restrictions on what you are backing up (apart from system files, since time machine isn't bootable. Then let TM do another backup to collect the files from these folders.
Then archive and install.