A sledge won't loosen it in its hole - you have to grab it with both hands and boogie back and forth, leaning on it hard in all directions, to gradually loosen it. Water well with hose a few hrs before doing this, if your soil is dry.
Antlers' method is the best one provided you 'get' it - however I am not sure whether it may be one of those things you have to see done, first?
Alternatively (and I'd do the wiggling thing as much as possible, first), get a piece of very strong rope and make a loop perhaps 12" across with it (exact size doesn't matter). Stick a heavy nail or other suitable bit of metal thru one of the holes in the t-post, as low down to the ground as you can, and put the loop around the t-post so it catches on the nail or whatnot. Now get a long strong lever (10' 4x4, or 2x6 on edge, or suchlike) and a fulcrum of suitable height (e.g. one or more cinderblocks. Put the lever end thru the remainder of the loop, prop it up on the fulcrum, and stand/bounce on the end of the lever til the post comes up.
Good luck,
Pat
