$'\E' represents the ASCII escape character (eg.
\033/CtrlV + Esc), rather than a backslash:
% printf '%x\n' \'$'\E'
One common use of this character is to indicate a control sequence: an alternate interpretation of a portion of subsequent bytes. For example, it's commonly used in shell prompts as part of an ANSI escape sequence to indicate that the terminal should colour some text, or by applications to ask the terminal to position the cursor, and much more.*
% printf '\033[36m%s\033[0m\n' 'this is in cyan'
this is in cyan
% printf '\033[2J' # clear the screen
* For most of these use cases, you usually want to use
tput instead, though, which is terminfo aware and somewhat more intuitive to use. These two basic examples should be pretty much universally understood, though.