It's not possible to recover the data once the phone has been formatted. However, there is a way but it implies to use a card reader. For example, if your data was stored on a SDcard then remove the SDcard and plug it to the computer using a card reader then use Recuva to attempt recovery operations. Perform a Deep Scan to increase the chances of finding more items. This is the possible way to recover the data.
Additionally, if you have your contacts and apps synced with an online account, simply add the account to your phone and connect to Internet. The sync operation should start automatically.