Did you really just format that external disk? Recover its data on macOS with data recovery software.

Method 1
Using software to recover deleted data
Step 1:
Download, install and launch the application
Step 2:
Scan the selected disk for files that can be recovered
Step 3:
Recover your files to a new storage location

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Updated 17 October. 2019
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Method 2
Recover deleted data from previoulsy made backups
Step 1:
Launch your backup and restore software
Step 2:
Determine if you have a backup of the data in question
Step 3:
Use the backup media to recover your selected data
Method 3
Employ a professional physical data recovery service
Step 1:
Carefully pack your machine to be shipped to the recovery service
Step 2:
Get used to life without your computer for a few days
Step 3:
Vow to never ignore those sounds from your hard drive ever again