You'll probably want to use some regex to parse the 'count: n' string from the file. Although my regex is kind of rusty, this pattern might help:
$file = fopen('text.txt', 'r+'); // Open the file for reading and writing into the variable $file.
$fileContents = file_get_contents($file); // Load the contents of the file to variable $fileContents.
$countString = preg_match('/count: [0-9]+/', $fileContents); // Find instances of string 'count: n' where n is an integer, load the string into $countString.
$count = preg_match('/[0-9]+/', $countString); // Find the integer from $countString, load into $count.
$count++; // Iterate count up one.
$newCountString = 'count: '.$count; // The 'count: n+1' string where n is the original integer.
$newFileContents = preg_replace('/count: [0-9]+/', $newCountString, $fileContents); // Find the string 'count: n' and replace with 'count: n+1' where n is the original integer.
fwrite($file, $newFileContents); // Write the new contents into the file.
fclose($file);
Good luck!