You can use following page and controller to serach user based on the email address,

You input email address and it shows you users with that email address.

<apex:page controller="SearchUSerByEmail">
  <apex:form > 
    <h1>Search User by email</h1>
      <apex:inputtext value="{!EnteredEmail}"/>
      <apex:commandButton value="Search" action="{!Searchuser}"/>
        <apex:pageBlock >
          <apex:Pagemessages rendered="{!ShowMessageFlag }"/>
           <apex:pageBlockTable value="{!usersList }" var="userRec" rendered="{!ShowTableFlag}">
            
             <apex:column headerValue="Email">
               <apex:outputField value="{!userRec.Email}"/>
             </apex:column>
            
             <apex:column headerValue="Name">
               <apex:outputLink value="{!userRec.id}"> {!userRec.Name}</apex:outputLink>
             </apex:column>

         </apex:pageBlockTable>
      </apex:pageBlock>
  </apex:form>
</apex:page>

public with sharing class SearchUSerByEmail {
public string EnteredEmail{get;set;}
public List<user> usersList{get;set;}
Public Boolean ShowMessageFlag{get;set;}
Public Boolean ShowTableFlag{get;set;}
ApexPages.Message myMsg;
    Public void Searchuser(){
    ApexPages.addMessage(new ApexPages.Message( ApexPages.Severity.info, 'There are no users with this email address'));

       ShowMessageFlag = false;
       usersList = New List<user>();
       usersList  = [select name,email from user where email=:EnteredEmail ];
       if(usersList.size()>0)
          ShowTableFlag= true;
       else
         ShowMessageFlag = True;
    }
}

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