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Tann's Notts County career was to go rapidly downhill though, after he picked-up a silly red card for two bookable offences on his fourth start for the club at home to Torquay.
He then broke his jaw on his return from suspension, an injury that left him on the sidelines for six weeks.
Thordarson showed great loyalty to the versatile defender - who also picked-up three bookings during his six appearences for Notts - during his recovery from this injury, as many had tipped that he would be released, saving the hard-up Magpies the expenditure of paying a non-playing player his wages.
Despite this, Tann has now opted to join Martin Ling's Orient side, just four days after he made his first-team return with the Magpies.
Though here on non-contract tersm, Tann becomes the fourth player to leave the club during the transfer window, following Glynn Hurst, Tony Scully and Matthew Gill to the Meadow Lane exit door.