Adding a number to a date

You need get_the_time, not the_time to get the date (the latter echo‘s the value). You also need to re-evaluate how you’re trying to calculate the end date – you can’t just “add” the number of days. What if the event length was 3 but the start date was the 31st?

if ( $event_length ) {
    // Get the unix timestamp of the post
    $post_time = get_the_time( 'U' );

    // Increase the timestamp by the event length
    $end_time = $post_time + $event_length * DAY_IN_SECONDS;

    // Conditional date format depending on if the event ends in the same month
    if ( date( 'm', $post_time ) !== date( 'm', $end_time ) )
        echo date_i18n( ' - M j', $end_time );
    else
        echo date_i18n( ' - j', $end_time );
}