Certain components of a software system are so critical, that not applying best development practices in those areas can slam a company with shockingly high legal, financial, customer, organizational and business costs - and all that slamming together all at the same time!
Storing passwords in plaintext and mailing them to customers is such a basic security mistake and has caused so many data breaches that it's not even funny now in 2015.
How would you feel if your bank sent you an email today stating that your savings account details, password and CVV may be compromised, and that you should check for any unauthorized transactions? Would you continue keeping your money in such a bank?
Guess whom managements blame when (and in 2015, it really has become a case of when, not if) data breaches occur?
This is not just another programming problem to be solved by googling and copy pasting some code snippets from the Internet.
This is one of those situations where a company's management may not realize the criticality of the problem, or may have simply assumed that their development team will do the right thing.
So as a software engineer with a code of ethics, it's upto you to step up and do the right thing the right way.
In my opinion, you should stop the coding, talk to your managers about the criticality of this area, upgrade your knowledge by yourself or with company sponsored training (preferably the latter), and only then come back to the coding.
Here are a few resources that will help. Don't skip reading the long form articles.
Understand the gravity of the business and management problem:
(PDF) 2015 cost of data breaches
A security code of ethics for developers and management
Understand the psychology behind why development orgs neglect security
Understand Design and Architecture issues:
OWASP authentication guide
Lessons, including password storage, from the Tesco breach
Understand implementation issues:
Why naive hashing is not enough
Secure password reset
Understand basics of password storage
Next understand why the above was good in 2007 but is no longer enough now in 2015
Security tips
OWASP authentication recipes
OWASP password guidelines
OWASP Secure Coding Practices
Read this discussion thread fully
Our Security FAQ (especially OWASP and Other Topics)