To keep Task Manager running but hidden from view, first start it and bring it to the foreground by pressing Ctrl-Shift-Esc or by right-clicking on the task bar and selecting Task Manager. In Task Manager, Choose Options, Hide When Minimized. Now, minimize Task Manager. Its icon will appear in the taskbar near the time display. To make Task Manager visible, double-click the taskbar icon. After each use, minimize it again--don't close it.
If you want Task Manager to always run in this fashion:
Right-click %SystemRoot%\System32\Taskmgr.exe
Click Create Shortcut
Right-click the shortcut link, select Properties and Run and pick Minimized.
Drag and drop the shortcut link to your profiles Startup folder, that is, %SystemRoot%\Profiles\yourlogonaccount\Start Menu\Programs\Startup folder.