gistfile1.js

var getAllPermutations = function(str){
  if(str.length < 2){
    return [str];
  }

  var result = [];

  for(var i = 1; i < str.length + 1; i++){
    var beginning = [str.slice(0, i)];
    var rest = getAllPermutations(str.slice(i));

    for(var j = 0; j < rest.length; j++){
      result.push(beginning.concat(rest[j]));
    }
  }

  return result;
};

var getAllAdditionSubtraction = function(nums){
  if(nums.length === 1){
    return nums;
  } else if (nums.length === 2){
    return [nums[0] - nums[1], nums[0] + nums[1]];
  }

  var rest = getAllAdditionSubtraction(nums.slice(0, nums.length - 1));
  var last = nums[nums.length - 1];
  var result = [];

  for(var i = 0; i < rest.length; i++){
    var single = rest[i];
    result.push(single + last);
    result.push(single - last);
  }

  return result;
};

var main = function(num){
  var permutations = getAllPermutations(num.toString()).map(function(str){
    return str.filter(function(chr){
      return chr !== "";
    }).map(function(num){
      return Number(num);
    });
  });

  var result = [];

  permutations.forEach(function(perm){
    result = result.concat(getAllAdditionSubtraction(perm));
  });

  return result;
};