Sometimes remnants of a closed window stick around for a while after an app is closed, and in those cases they can be cleared up by refreshing the portion of the display where the leftover image fragment is. Two things to try before Hal's suggestion:
1
) Go to Start -> Settings -> Taskbar, and check "Auto hide," and then tap OK. Now press the Windows key to bring up the taskbar again, and see if you can see the system tray now.
2
) If 1
) fails, try a soft reset.