tweet.html

<form action="tweet.php" method="post">
 <p>Your tweet: <input type="text" name="tweet" /></p>
 <p>Your @(handle): <input type="text" name="handle" /></p>
 <p><input type="submit" /></p>
</form>

tweet.php

<?php

require 'vendor/autoload.php';

$consumerKey = 'xxxxxxxxxxxxxxxxxxxxx';
$consumerSecret = 'xxxxxxxxxxxxxxxxxxxxx';
$accessToken = 'xxxxxxxxxxxxxxxxxxxxx';
$accessTokenSecret = 'xxxxxxxxxxxxxxxxxxxxx';

$twitter = new Twitter($consumerKey, $consumerSecret, $accessToken, $accessTokenSecret);
try {
        $tweet = $twitter->send($_POST['tweet'].' by '.$_POST['handle']  );

} catch (TwitterException $e) {
        echo 'Error: ' . $e->getMessage();
        }

Assuming your Twitter library returns false on a the send method in the event of a failure (which I'd hope it does), you could avoid try/catch by doing something like:

$tweet = $_POST['tweet'].' by '.$_POST['handle'];

if(!$twitter->send($tweet){
  // error handling
}