If you're going to use seek, read the documentation, the first graf of which explains how to increment the position:

 seek FILEHANDLE,POSITION,WHENCE
        Sets FILEHANDLE's position, just like the "fseek" call of
        "stdio". FILEHANDLE may be an expression whose value gives the
        name of the filehandle. The values for WHENCE are 0 to set the
        new position *in bytes* to POSITION; 1 to set it to the current
        position plus POSITION; and 2 to set it to EOF plus POSITION,
        typically negative. For WHENCE you may use the constants
        "SEEK_SET", "SEEK_CUR", and "SEEK_END" (start of the file,
        current position, end of the file) from the Fcntl module.
        Returns 1 on success, false otherwise.

Assuming your really intend to do something like this:

#!/usr/bin/perl
use 5.016;
use Data::Dumper;

#1033562  (and id num_qqq.txt, idnum_exp.txt)

=head

file 1033562_exp.txt
exp.txt    0
foo    3
bar    1
table    3
quux    3
fail    2

file 1033562_qqq.txt
qqq.txt    0
fail    2
nope    1
foo    3
insert    1
bar    1
quux    3
table    3
tambourine    2
fred    14

=cut

open(INDB, "1033562_exp.txt") or die "Can't open exp file, $!"; 
open(QQQ, "1033562_qqq.txt") or die "Can't open data file, $!";

my (@search, @therecs);

while(<INDB>) {
    my $search = $_;
    chomp($search);
    say "\$search at Ln28: $search";
    push @search, $search;
    seek(INDB, 0, 0);
}

print "\n\n";

while(<QQQ>) {
    my ($ma,$id);
    my $therec = $_;
    say "Both elements of \$therec at Ln36: $therec";
       chomp($therec);
    ($ma,$id ) = split(/\t/, $therec);
    push @therecs, (" $ma  " . "| $id |");
    my $Qpos=tell QQQ;
    say "\n\t POS in QQQ: $Qpos \n";
}

say "\n \t array search next:";
say Dumper @search;

say "\n \t Array @therecs next:";
say Dumper @therecs;
[download]

</c>

Identifying the matches is left as an exercise to the SOPW. %hash might be an approach; so too might what you originally suggest but didn't implement-- walking the arrays in parallel. Both are well documented in threads here in the Monastery.