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https://jsfiddle.net/w0pohLeb/3/

<style>
   #login {
     display: none;
   }
</style>


<input type="text" id="username" required="true">
<input type="email" id="email" required="true">
<button type="submit" id="login">
  Sign Up
</button>


<script>
  
$(document).ready(function() {
  if ($('#email').val().trim().length === 0 && $('#username').val().trim().length === 0) {
    $('#login').hide();
  }
  else {
    $('#login').show();
  }
  $("#email, #username").keyup(function () {
    if ($('#email').val().trim().length === 0 && $('#username').val().trim().length === 0) {
      $('#login').hide();
    }
    else {
      $('#login').show();
    }
  });
});  
  
</script>