Примерно решение

exam_hour = int(input())
exam_minute = int(input())
hour_of_arrival = int(input())
minute_of_arrival = int(input())

exam_time = exam_hour * 60 + exam_minute
arrival_time = hour_of_arrival * 60 + minute_of_arrival

time_difference = arrival_time - exam_time
my_time = ''

if time_difference < -30:
    my_time = 'Early'
elif time_difference <= 0:
    my_time = 'On time'
else:
    my_time = 'Late'

result = ''
if time_difference != 0 or time_difference == 0:
    hours = abs(time_difference) // 60
    minutes = abs(time_difference) % 60
    if hours != 0 and minutes < 10:
        minutes = f'0{minutes}'

    if my_time == 'Early':
        print('Early')
        if hours <= 0:
            print(f"{minutes} minutes before the start")
        else:
            print(f"{hours}:{minutes} hours before the start")
    elif my_time == 'On time':
        if hours == 0:
            print('On time')
            print(f"{minutes} minutes before the start")
        elif hours > 0:
            print('On time')
            print(f"{hours}:{minutes} hours before the start")
        else:
            print('On time')
    else:
        print('Late')
        if hours <= 0:
            print(f"{minutes} minutes after the start")
        else:
            print(f"{hours}:{minutes} hours after the start")