How can I reset my iPad 2 without the password to my old deleted email?

Resetting you iPad will require the AppleID credentials that were last used to successfully activate the iPad. If these have also been forgotten, they can be recovered here:

https://iforgot.apple.com

To recover your credentials, you’ll need access to one of the following:

• Your primary email address mailbox that corresponds with your AppleID
• Any of the secondary/recovery email addresses that should be configured for your AppleID account
• Any of the trusted telephone numbers (fixed line or Cellular/Mobile) that are associated with your AppleID

Unless you AppleID account has not been fully/correctly configured, or has been seriously neglected, recovery of the AppleID and password should not be difficult. If your AppleID account has been properly set-up, loss of access to the primary email address (that identifies your AppleID account) will not, of itself, prevent account recovery.

More information about recovery of your AppleID:

If you forgot your Apple ID - Apple Support

More information about recovery of your AppleID password:

If you forgot your Apple ID password - Apple Support

When you recover access to your credentials, you would be well advised to log-in to your AppleID account from a web browser - and verify/update any email addresses and trusted telephone numbers:

https://appleid.apple.com

As a last resort:

How to use account recovery when you can’t reset your Apple ID password - Apple Support

If you mean that you are currently locked out of your iPad, you will need to restore it in order to regain access to it again. Unfortunately, the restore process will completely erase your iPad and you will lose any data on it. The only way to restore it, would be from a backup.

Forget this very old iPad, at this point.

It is a 10-year old device that has not been supported, by Apple, in 6 years and has NO third party app support, any longer and is completely obsolete.

If you cannot get into this iPad, then no one will, either.

Just forget about this ancient iPad.

Just properly recycle this device by dropping off at your nearest Apple Store location or recycle with a local electronics recycler.

Sorry & Good Luck to You!