1st Project Guess between 1 and 20

[MiNigle]

Hi, first time on python (only dabbled with VBA previously) and I've done the cliche guessing game (sorry!) Taken me a few days.

I've tried to go further and make it a more robust using functions. I'm finding it really hard to get my head around functions and how to use them with arguments. My code is a little as a result of trial-and-error and I don't quite understand why some of it works. If anyone's willing, could I have some feedback on whether the code is 'neat' or unnecessary or if I've committed any python faux pas? Thank you very much.

# Guessing Game

def string_or_integer(guess):
    while True:
        if guess in ('quit', 'Quit'):
            print('Bye bye!')
            sys.exit()
        elif not guess in ('quit', 'Quit'):
            try:
                return int(guess)
            except ValueError:
                try:
                    float(guess)
                    print("Please use whole numbers")
                    guess = input('>>> ')
                except ValueError:
                    print ("This is not a number. Please enter a number between 1 and 20")
                    guess = input('>>> ')

def game():
    guess = input('>>> ')
    guessInt = string_or_integer(guess)
    if (guessInt == rNum):
        print('Congratulations! You won!')
        sys.exit()
    elif (guessInt > 20):
        print('Way too high! Guess between ONE and TWENTY')
        game()
    elif (guessInt < rNum):
        print('Try a higher number')
        game()
    elif (guessInt > rNum):
        print('Try a lower number')
        game()

import random
import sys
rNum = random.randint(1,20)
print('Welcome to the Guessing Game!\nGuess a number between 1 and 20\nTo give up, type "quit"')
game()