To do something to each element of an array, you need a loop over each element of the array. I don't know what's special about for loops that they need to be avoided. Maybe if you told us that, we could help you better.

I wouldn't use a for loop anyway. I'd use a counting loop. The syntax of a counting loop is much simpler than that of a for loop, it's faster do to the much smaller number of opcodes, and it also uses a constant amount of memory. (Mostly for the first reason. The other two are bonuses.)

Counting loop (an optimised form of foreach loop):

$a[$_] -= $b[$_] for 0..$#a;
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Foreach loop:

$a[$_] -= $b[$_] for (),0..$#a;
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Using map like a foreach loop:

map { $a[$_] -= $b[$_] } 0..$#a;
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my $i = @a; $a[$i] -= $b[$i] while $i--;
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Goto loop:

my $i = @a;
goto CHECK;
BODY:  $a[$i] -= $b[$i];
CHECK: goto BODY if $i--;
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Recursion loop:

sub subarray {
    my ($a, $b) = @_;
    local *_helper = sub {
        my $i = $_[0];
        return if !$i--;
        $a->[$i] -= $b->[$i];
        _helper($i);
    };
    _helper(0+@$a);
}

subarray(\@a, \@b);
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Recursion loop, take 2:

sub subarray {
    my ($a, $b) = @_;
    local *_helper = sub {
        return if !@_;
        $_[0] -= $_[-1];
        shift; pop;
        &_helper;
    };
    _helper(@$a, reverse(@$b));
}

subarray(\@a, \@b);
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pairwise loop:

use List::MoreUtils qw( pairwise );
@a = pairwise { $a - $b } @a, @b;
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Update: Added more alternatives :)