The easiest solution is if earthlink email offers an auto-forwarding email copy to an external mail account. GMail does. Though brings up an important consideration in that one should not use a primary email account from an internet service provider (ISP). It's to their advantage to make it difficult, if not possible to auto forward emails as it keeps you locked in to their service. Just to avoid the hassles transferring archived mails and having to change email addresses in existing internet accounts.
GMail does have a feature to read emails from other service provider accounts. That may be the easiest method if GMail supports earthlink email? See
Check emails from other accounts.
In GMail webmail, click the Gear icon and go to
Accounts and Import > Check mail from other accounts: > Add a mail account.
Note that the built-in Outlook email client in WIN10 can also read/write emails from other email providers. Personally, I prefer free Outlook.com email account as it allows you to create separate email alias that forward to your primary account. This keeps your primary email address hidden from most spammers. When the alias email account is no longer useful, delete it and create more if desired.
One downside is that Outlook.com spam filter is somewhat aggressive, and can send legit emails to Junk folder. So need to check routinely, or set up contact or filter rules.