bruteForceFormula.php

<?php
$l = range('A', 'I');

for($i=123456789; $i<=987654321; $i++){
 $a = str_split((string)$i);
 if(9 <> count(array_unique($a))) continue;
 if(in_array('0', $a)) continue;

 $a = array_combine($l, $a);
 if($a['A'] - $a['B'] != $a['C']) continue;
 if($a['A'] + $a['B'] != $a['D']) continue;
 if($a['B'] * $a['E'] != $a['F']) continue;
 if($a['G'] - $a['H'] != $a['I'] / $a['B']) continue;

 echo "ABCDEFGHI\n$i\n";
}