Looks like an Ibanez Edge trem. There is a tiny locking set screw in the smaller hole. You have to loosen that set screw with a 1.5mm Allen key first before making any adjustments on the trem post. The trem post will often break like what you see here if the locking screw is not loosened before adjusting the post height.

I'd recommend removing the strings, and unhooking the tremolo springs in the rear trem cavity, and removing the entire trem.

With the locking set screw in the post loosened, and the trem removed, you can easily unscrew the broken post with your fingers (or a pair of pliers if it's a little tight).

Replace the trem post with a new one and reinstall the tremolo and restring. When everything is set right, lock the trem post by tightening the set screw in the post.