Number-guessing game using functions
What you have is very good and it certainly functions as expected. I have just a few ideas to consider implementing (more in relation to the game than the code):


Print the number ranges for each difficulty at the start, so that the user knows what range to guess in.
Check if the guess is outside the range.
Count the number of guesses and report back to the user at the end.
Edit the prompts slightly so user knows when input is expected.


I have shown my code below, implementing these features. I reduced it to a single function (to avoid having to use global variables). I have used a dictionary to store the top end of the range of each difficulty (difficulty_ranges) so this can be checked easily later, using fewer if else checks.

I also corrected a few PEP8 style warnings (spacing, use snake case instead of camel case for function name etc).

import random


def number_guess_game():
    # Set up main variables
    guesses = 0
    difficulty_ranges = {'e': 20, 'm': 50, 'h': 100}

    while True:
        difficulty = input(
            "Type E, M or H for easy (0-20), medium (0-50), or hard (0-100) number range:\n").lower()
        try:
            number = random.randint(0, difficulty_ranges[difficulty])
            break  # Need to break the while loop here
        except KeyError:
            print("Incorrect input! Choose again...")  # Encourage user input

    while True:
        try:
            guess = int(input("Your guess: "))
            guesses += 1
            if number == guess:
                print("Correct guess! You used {} guesses.".format(guesses))
                return number_guess_game() if input(
                    "Play again? Press Y to play again or any key to exit.").lower() == 'y' else 0
            elif guess &lt; 0 or guess &gt; difficulty_ranges[difficulty]:
                print("Your guess was out of range!")
            else:
                print("Too High. Guess again..." if number &lt; guess else "Too Low. Guess again...")
        except ValueError:
            print("Must be an integer value.\n")


def main():
    number_guess_game()


if __name__ == '__main__':
    main()


I should add that I am not a Python expert, so other users will likely provide more useful information on the code. I think your layout is good and the logic is easy to follow. I wanted to suggest a few of these extra features as it is a game and these may improve the experience.