[SuperZen]

Примерно так, но надо проверять...

let express = require("express");
let app = express();
var nodemailer = require("nodemailer");

app.get('/', function (req, res) {
  sendEmail('f@ya.ru', '1').then(() => {
    console.log('sended')
    res.send('sended')
  }).catch((error) => {
    console.log(error)
    res.send('error')
    // res.send(error.message)
  })
  // console.log(sendEmail('f@ya.ru', '1'));
});

function sendEmail(email, password) {
  return new Promise((resolve, reject) => {
    nodemailer.createTestAccount((err, account) => {
      errortext = err;
      let transporter = nodemailer.createTransport({
        host: 'smtp.ethereal.email',
        port: 587,
        secure: false,
        auth: {
          user: account.user,
          pass: account.pass
        }
      });
      let mailOptions = {
        from: '"Heano" <games.1212@yandex.ru>',
        to: email,
        subject: 'Регистрация ✔',
        text: 'Твой пароль: ' + password,
        html: 'Твой пароль:<b> ' + password + '</b>'
      };
      transporter.sendMail(mailOptions, (error, info) => {
        if (error) {
          reject(error)
          // return false;
        }
        else {
          resolve()
          // return true;
        }
      });
    });
  })
}

let server = app.listen(2800, () => console.log("Работа пошла"));