Thats really quite easy to do with PHP.

fopen will open a file:
PHP Tutorials: Opening a file with fopen

so something like this would join the 2 files together & create a 3rd new file:

PHP Code:

$txt_1 = fopen("text_dir/file_1.txt", "r");
$txt_2 = fopen("text_dir/file_2.txt", "r");
$new_txt = $txt_1 . $txt_2;
fclose($txt_1);
fclose($txt_2);

$new_file = fopen('file_path/new_text.txt', 'w') or die("can't open file");
fwrite($new_file, $new_txt);
fclose($new_file); 


I haven't tested this, but it should work.