$string !~ s/\d{10}//g;

##</code><code>##

if ($string !~ s/\d{10}//g) {
   print "String unchanged: couldn't find 10 digits.\n";
   # do stuff to deal with regex failure
}
else {
   print "All cases of 10 digits have been deleted.\n";
}

##</code><code>##

if (not $string =~ s/\d{10}//g) {
unless ($string =~ s/\d{10}//g) {