I am facing a problem when I just know an email of a user and not their username in Stack Overflow. because it may be something else.
There should be a feature to search users by email.
That would be a huge privacy breach: Stack Overflow's promise is that they will never reveal your E-Mail address. Making profiles searchable by E-Mail would seriously undermine this.
The solution to this problem is to E-Mail the person in question, and ask them for the URL to their Stack Overflow profile.
Why not ask the person by email?
There is no way for normal users to search by email. Emails are private data, and the user expects SE to keep them private. And privacy includes the ability for people to associate them with the email via search. Some people may not even want to be searchable by email.
Note that mods can search by email.
Funny that SE set this to [status-denied], considering they have no problem publishing their users' email hashes. This feature is easy to implement using data-explorer. So I suggest tagging this with [status-completed].
They publish email hashes to implement gravatar, see Is Gravatar a privacy risk?