You cannot subtract strings.
$today should be time(), and $uptime MUST be an integer. Then you can subtract and create $uptime1. That will give you the number of seconds $uptime is which you can format into whatever display.
If you have 5.3+, you can use the dateinterval.
$dtUptime = new DateTime($json_array['up_time']); // this now assumes a string GNU valid format
$dtNow = new DateTime();
$diDiff = $dtNow->diff($dtUptime, true);
print $diDiff->format("Uptime: %a days");