I think it might be simple as something like this, connected to OnBeforeDocFormSave:

$start = strtotime($resource->getTVValue('start_date'));
$end = strtotime($resource->getTVValue('end_date'));

if ((!empty($start)) && (!empty($end)))
    if ($end < $start) {
        return (array('End date must be later than start date'));
    }
}

return;

It should display the error message, but I've never tested it.

This will check both new and existing resources on save. If you don't want that, you can put something like this at the top:

if ($mode === modSystemEvent::MODE_NEW) {
    return '';
}

You may also want to add a test of $resource->get('parent') or $resource->get('id') at the top to limit it to specific resources.