No, you'll need the information from that W2. If you can't get it from your former employer then you can get the W2 from the IRS (although you will still not have the employer ID number).
In order to get information from the IRS go to the IRS website here and create an account. You'll have to jump through a few hoops but then you'll be able to download any information that has your social security number on it.
r.newton.d@gmail
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