How to jump back to NERDTree from file in tab?

Ctrl-ww

This will move between open windows (so you could hop between the NERDTree window, the file you are editing and the help window, for example... just hold down Ctrl and press w twice).

If you use T instead of t there is no need to jump back because the new tab will be opened, but vim's focus will simply remain within NERDTree.

NERDTree opens up in another window. That split view you're seeing? They're called windows in vim parlance. All the window commands start with CTRL-W. To move from adjacent windows that are left and right of one another, you can change focus to the window to the left of your current window with CTRL-w h, and move focus to the right with CTRL-w l. Likewise, CTRL-w j and CTRL-w k will move you between horizontally split windows (i.e., one window is above the other). There's a lot more you can do with windows as described here.

You can also use the :NERDTreeToggle command to make your tree open and close. I usually bind that do t.

Ctrl+ww cycle though all windows

Ctrl+wh takes you left a window

Ctrl+wj takes you down a window

Ctrl+wk takes you up a window

Ctrl+wl takes you right a window