Your task is recursive in nature. Here is one way to approach it:

#!/usr/bin/perl

use strict;
use warnings;

use Data::Dumper;

my %tifs = (
    '2014-06-01 00:00:00' => 'file_01.tif',
    '2014-06-02 00:00:00' => 'file_02.tif',
    '2014-06-03 00:00:00' => 'file_03.tif',
    '2014-06-04 00:00:00' => 'file_04.tif',
);

hashmath( sort( keys( %tifs ) ) );

exit;

sub hashmath {
    my @times = @_;

    print '@times has ' . scalar( @times ) . " elements\n";
    print Dumper(\@times);

    my $time = shift( @times );
    for my $next_time ( @times ) {
        # do math and whatever here
        print "Subtracting $time from $next_time\n";
    }
    hashmath( @times ) if @times > 1;

    return;
}

__END__
[download]

$ perl hashmath.pl 
@times has 4 elements
$VAR1 = [
          '2014-06-01 00:00:00',
          '2014-06-02 00:00:00',
          '2014-06-03 00:00:00',
          '2014-06-04 00:00:00'
        ];
Subtracting 2014-06-01 00:00:00 from 2014-06-02 00:00:00
Subtracting 2014-06-01 00:00:00 from 2014-06-03 00:00:00
Subtracting 2014-06-01 00:00:00 from 2014-06-04 00:00:00
@times has 3 elements
$VAR1 = [
          '2014-06-02 00:00:00',
          '2014-06-03 00:00:00',
          '2014-06-04 00:00:00'
        ];
Subtracting 2014-06-02 00:00:00 from 2014-06-03 00:00:00
Subtracting 2014-06-02 00:00:00 from 2014-06-04 00:00:00
@times has 2 elements
$VAR1 = [
          '2014-06-03 00:00:00',
          '2014-06-04 00:00:00'
        ];
Subtracting 2014-06-03 00:00:00 from 2014-06-04 00:00:00
$
[download]