Flying into MAN on US and then wanting to go out of Luton. Would this be an easy thing to do by train? About how much would it cost? Would a bus be better or cheaper?

I did an internet search and an not sure if the train schedule was actually airport to airport (???) or city to city, but it appears that this can be done in about 3.5 - 4.0 hours. What would be the best way to buy this type of ticket? It appeared that advance purchases are as low as 16 pounds.

Can it be done electronically?

Thanks for the help.