You can create a custom Timer class and start it in a diffrent thread. Once the timeout occurs (after 10 seconds), you can send a SIGINT signal back to the parent thread, which will raise the KeyboardInterrupt exception that we catch in the main() function. Otherwise you can stop the Timer, after user enters the second input in the right time, which will then stop the Timer thread. Further, we can check if the KeyboardInterrupt happened due to timeout or user action.
Note: While we are sending the signal to the main process, we also need to check, on which platform we are running the programm. See signal.CTRL_C_EVENT and signal.SIGINT.
Demo: https://repl.it/repls/StandardBuoyantProtools
Solution:
import time
import threading
import os
import signal
class Timer(threading.Thread):
    _timeout = False
    _timer = 0
    _stopped = False
    def __init__(self, delay):
        super(Timer, self).__init__()
        self.restart(delay)
    def is_timeout(self):
        return self._timeout
    def stop(self):
        self._stopped = True
    def restart(self, delay):
        self._stopped = False
        self._timer = time.time() + delay
    def run(self):
        while not self._stopped:
            time.sleep(0.1)
            if time.time() >= self._timer:
                break
        if not self._stopped:
            self._timeout = True
            # check os name
            if os.name == 'nt':
                # we are on Windows
                os.kill(os.getpid(), signal.CTRL_C_EVENT)
            else:
                # we are on a Posix/Unix (or very unlikely on java) system
                os.kill(os.getpid(), signal.SIGINT)
def main():
    first_input = input('First input:')
    delay = 10
    timer = Timer(delay)
    timer.daemon = True
    try:
        print('\nStarting the timer for the second input %r second(s)' % delay)
        timer.start()
        second_input = input('Second input:')
        print('\nWell done. Stopping the timer!\n')
        timer.stop()
        print('Input values: %r %r\n' % (first_input, second_input))
        # do your stuff here...
    except KeyboardInterrupt:
        if timer.is_timeout():
            print("\nTimeout!")
        else:
            print("\nUser interrupted the input")
main()