Carbon provides the function weekOfYear to get the week of the year as integer. However I need to go the other way round to get the a date based on the year + the week of the year.
Carbon::now()->weekOfYear(); // todays week of the year
Carbon is a wrapper for PHP's DateTime, so you can use setISODate:
$date = Carbon::now(); // or $date = new Carbon(); $date->setISODate(2016,42); // 2016-10-17 23:59:59.000000 echo $date->startOfWeek(); // 2016-10-17 00:00:00.000000 echo $date->endOfWeek(); // 2016-10-23 23:59:59.000000