We all know Lumia 810’s Firmware variant is RM-878. But on FCC there is one recent entry with name RM-878X and it has passed test for LTE 1700 Frequency (T-Mobile’s LTE frequency). This devices has a final action date of December.The original RM-878 without LTE band and final action date in October is also listed there.
The RM-878X has confidentiality till 24th June, hence no photos are available. So, may be be T-Mobile is going to get LTE variant of Lumia 810 from June or it may be a new device, possibility of which is less. Or, as some recent rumors have it, may be a software update will enable the LTE on Lumia 810 in June.