$n = [1,2,3,4,5,6,7,8,9];//исходный массив
$sum = 14;//сумма

function sum($pos_n, $pos_s, $prev_sum, $s) {
  global $n,$sum;
  for ($i = $pos_n; $i < count($n); $i++) {
    $cur_sum = $prev_sum + $n[$i];
    if ($n[$i] >= $sum || $cur_sum > $sum) {
      continue;
    }
    if ($cur_sum == $sum) {
      $s[$pos_s] = $n[$i];
      foreach ($s as $v) {
        echo $v . ' ';
      }
      echo '<br>';
      return;
    } else {
      $s[$pos_s] = $n[$i];
      sum($i + 1, $pos_s+1, $cur_sum, $s);
    }
  }
}

rsort($n);
sum(0,0,0,[]);