Task.js

function skipLeadingZeros (string) {
  var str = ''
  var start = 0
  var end = string.length

  while(start < end && string[start] === '0'){
    start ++
  }

  while(start < end){
    str += string[start]
    start += 1
  }

  return str
}

// since input string contain only '0' to '9' we can use parseInt safely
function sumStrings (string1, string2) {
  var carry = 0
  var ans = ""
  var start1
  var start2
  var digit1
  var digit2
  
  string1 = skipLeadingZeros(string1)
  string2 = skipLeadingZeros(string2)
  start1 = string1.length - 1
  start2 = string2.length - 1

  while(start1 >= 0 && start2 >= 0) {
    digit1 = parseInt(string1[start1])
    digit2 = parseInt(string2[start2])
    ans += (digit1 + digit2 + carry) % 10
    carry = Math.floor( (digit1 + digit2 + carry) / 10 )
    start1 -= 1
    start2 -= 1
  }

  while(start1 >= 0) {
    digit = parseInt(string1[start1])
    ans += (digit + carry) % 10
    carry = Math.floor( (digit + carry) / 10)
    start1 -= 1
  }

  while(start2 >= 0) {
    digit = parseInt(string2[start2])
    ans += (digit + carry) % 10
    carry = Math.floor( (digit + carry) / 10)
    start2 -= 1
  }
  
  if (carry !== 0) {
    ans += carry
  }
  
  return ans.split('').reverse().join('')
}

function testRunner (expectedValue, valueFromTest) {
  // check type also use ===
  if (expectedValue === valueFromTest) {
    return 'passed'
  } else {
    return 'failed'
  }
}


// test cases for methods

testRunner(skipLeadingZeros('000123'), '123')
testRunner(skipLeadingZeros('001023'), '1023')
testRunner(skipLeadingZeros('000120300'), '120300')


testRunner(sumStrings('1', '2'), '3')
testRunner(sumStrings('800', '9567'), '10367')
testRunner(sumStrings('99', '1'), '100')
testRunner(sumStrings('00103', '08567'), '8670')
testRunner(sumStrings('50095301248058391139327916261', '81055900096023504197206408605'), '131151201344081895336534324866')
testRunner(sumStrings('00000000', '8567'), '8567')
testRunner(sumStrings('99999', '99999'), '199998')