First, I wanted to get now() in Carbon. But I can't. I don't know why.
The Instantiation section of the Carbon manual provides these examples:
$carbon = new Carbon(); // equivalent to Carbon::now()
$now = Carbon::now();
They're equivalent, so you have to pick one rather than using both.
You already have a powerful dedicated data type for dates—you should make use of it. Thus this:
date('Y-m-d H:i:s');
... serves no real purpose and only adds confusion.
As about getting differences, there's a whole Difference chapter in the manual. It should be pretty straightforward once you use the appropriate types.