Does T100 Passenger Backrest Fit A 2010 Se?

I have an offer of a T100 back rest. Does anyone know if it can fit a 2010 SE, and if so, without losing the chrome luggage rack?

I have just fitted the standard T2306989 chrome luggage rack to my 2010 SE.
My daughter riding pillion finds it worse to reach for a comfortable ride - on rural English roads.

Thus I am looking at fitting a back rest but it looks like the Triumph one only fits with a sissy bar and probable won't be compatible with the rack.

Any advice greatly appreciated.