set_error_handler allows you to specify a user-defined error handling function for deciding what to do with certain (but only non-fatal) errors. You can then handle specific types of errors in any fashion you deem necessary, for example notifying a system administrator via email, or saving to a specific log file. See:  PHP Doc for further details. 
With regards to your request you could the following approach:
function myErrorHandler($errno, $errstr, $errfile, $errline)
{
  if (!(error_reporting() & $errno)) {
    // This error code is not included in error_reporting
    return;
  }
  switch ($errno) {
    case E_USER_ERROR:
    case E_ERROR:
    case E_COMPILE_ERROR:
      echo "<b>My ERROR</b> [$errno] $errstr<br />\n";
      echo "  Fatal error on line $errline in file $errfile";
      echo ", PHP " . PHP_VERSION . " (" . PHP_OS . ")<br />\n";
      echo "Aborting...<br />\n";
      emailErrorFunction($errno,$erstr,$errfile,$errline);
      exit(1);
      break;
  default:
      echo "Unknown error type: [$errno] $errstr<br />\n";
      break;
  }
/* Don't execute PHP internal error handler */
  return true;
}
// Report all errors
error_reporting(E_ALL);
// User a custom error handler to print output
set_error_handler( 'myErrorHandler' );
As that error-handling does not work for Fatal Errors (Parse errors, undefined functions etc.), you need to tape this with register_shutdown_function as outlined in a related question: