The exclusive-or operator (^) between strings returns \x00 for each matching pair of characters, and a different value for non-matching characters. Thus, 'Perl' ^ 'Perl' would return '\x00\x00\x00\x00'. Matching a returned string for [^\x00] will show where the strings differ. In your case, only the first difference is requested. Given this, consider the following that uses your data:
use warnings;
use strict;
open my $fh1, '<', 'first_file.txt' or die $!;
open my $fh2, '<', 'second_file.txt' or die $!;
while ( my $s1 = <$fh1> ) {
chomp $s1;
chomp( my $s2 = <$fh2> );
( $s1 ^ $s2 ) =~ /[^\x00]/;
substr( $s2, $-[0], 0 ) = '+' if defined $-[0];
print $s2, "\n";
}
close $fh2;
close $fh1;
Output:
amaya+mAn
vismaya+mAn
soura+mA
kamal+An
The variable $-[0] contains the position of the last match, which is passed to substr to insert a + at the location of the first difference between the two strings.