tangent already solved it for you. Here's a recap with some style changes and security amendments.

use strict;
use warnings;

# Uninitialized errors are normal for this kind of CGI.
no warnings "uninitialized";

# LWP was not being used.

use CGI;

# Do not leave this in the script production.
use CGI::Carp qw(fatalsToBrowser);

# ->new is better; search indirect object syntax problems.
my $q = CGI->new;

print $q->header, $q->start_html;

my $previousTotal = $q->param('sumTotal');

# Printing raw user input is a serious security problem.
# Adding 0 will numify and clobber strings like "<script />"
print $q->h2("Previous Total:", $previousTotal + 0);

my $currentTotal = $previousTotal + 2;

# Don't need "print" for every op and please do not put "br"s
# everywhere for formatting.
print $q->h2("Current Total:", $currentTotal),
    $q->start_form( -name   => 'addition',
                    -method => 'GET' ),
    $q->hidden( -name => 'sumTotal',
                -override => 1,
                -value => $currentTotal ),
    $q->submit( -name => 'button',
                -value => 'Add 2' ),
    $q->end_form,
    $q->end_html;

exit 0;
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