Calculate difference between two times
Both the function name and the docstring are clear and informative. Good job there! However, there are a couple of typos in the examples. The function requires strings as input but the examples use ints. For example time_difference(1100, 1310) should be time_difference('1100', '1310'). A tool like doctest can help you check for mistakes like this automatically.

Generally people don't check the types of arguments in python. You are right to document the types expected by the function but after that I would just use the objects as if they are the right type and let python throw an error if they aren't. I say this because type checking often gets in the way of duck typing and reduces the flexibility and generality of your code. For example, in python 2.x, isinstance(time_start, str) returns False for unicode strings (isinstance(time_start, basestring) is a better alternative).

The try/except is unnecessary as you are simply reraising every exception you catch.

Rather than trying to parse the strings yourself (which is quite error prone as AdHominem pointed out), you can use the datetime library instead.

If we apply these changes the result looks like:

from datetime import datetime

def time_difference(time_start, time_end):
    '''Calculate the difference between two times on the same date.

    Args:
        time_start: the time to use as a starting point
        time_end: the time to use as an end point

    Returns:
        the difference between time_start and time_end. For example:

        &gt;&gt;&gt; time_difference('1500', '1600')
        60

        &gt;&gt;&gt; time_difference('1100', '1310')
        130
    '''

    start = datetime.strptime(time_start, "%H%M")
    end = datetime.strptime(time_end, "%H%M")
    difference = end - start
    minutes = difference.total_seconds() / 60
    return int(minutes)