you are substracting strings.
You should translate these strings into unix timestamp, and then you will be able to do the substraction:
//Split the strings into hours, minutes and seconds integers
list($h1, $m1, $s1)=explode(':', $time1);
list($h2, $m2, $s2)=explode(':', $time2);
//Get the timestamps
$timestamp1=mktime($h1, $m1, $s1, 0, 0, 0);
$timestamp2=mktime($h2, $m2, $s2, 0, 0, 0);
//Do the substraction
$substract=$timestamp1-$timestamp2;
//Show the result
printf("<h1>The result is %s</h1>\n", strtotime("%H:%M:%S", $substract));