Note that many websites have their own advertising, unrelated to adware.
Search-Explorer is an IE toolbar providing the usual search features.
The program may be removable by opening the 'Downloaded Program Files' folder inside the Windows folder and removing the entry corresponding to Search-Explorer. (To find where each object came from, right-click it and choose 'Properties'.)
Ad-Aware reflist 032-23.06.02 and up can also remove it.