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If you don't know the email address for login, or you do but have no access to read incoming email, then you have no way in. Even Atlassian cannot get you in - the minimal requirement for an Atlassian account is an email address that you can read email from.
All you can do is move to a new email address that you can read. I would start with the account you have got that created the question here (I assume you are getting emails for this) and ask Atlassian to add that account to the administrators of your Trello site.
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