I use Windows 8.1 Professional edition. I accidentally clicked the Forget network button instead of Close in the network panel for wireless connections. Now my PC can't discover the wireless network connection that I removed.
How can I restore the connection that I deleted?
You cannot restore a "forgotten" (aka deleted) wireless network definition.
Instead you need to add it back the same way you did the first time you saved it. The easiest way to do this is to be in range of the wireless network, then connect to it and provide the proper passphrase, being sure to enable the connect automatically check box.