How can I delete all files from or format an external SD card programmatically in Android?

Question

I have done done lots of googling and searching here on StackOverflow for an answer to my question. I have seen the many posts about a recursive file deletion method (like this, this, and this), but none of these have worked for me. I am using this method to find my SD card (which is /storage/0000-0000).

private void wipeSDCards() {
    File storage = new File("/storage");
    File[] storageSubDirs = storage.listFiles();
    for (File storageSubDir : storageSubDirs) {
        try {
            boolean storageSubDirIsEmulated = Environment.isExternalStorageEmulated(storageSubDir);
            boolean storageSubDirIsRemovable = Environment.isExternalStorageRemovable(storageSubDir);

            if (!storageSubDirIsEmulated && storageSubDirIsRemovable) {
                deleteStuff(storageSubDir);
            }
        } catch (IllegalArgumentException iae) {
            LoggingUtil.i(MyClass.class, String.format(Locale.US, "FAILED ON: %s", storageSubDir.getAbsolutePath()));
        }
    }
}

private void deleteStuff(File fileOrDirectory) {
    // things I have tried ....
}

To delete the files on the SD card I have tried:

File fileToDelete = new File('path.to.file');
fileToDelete.delete();

But that doesn't work. I have tried:

Files.delete(fileToDelete.toPath());

But that doesn't work. I have tried:

application.getContentResolver().delete(uri, null, null);

But that doesn't work either. I have placed this print statement just before all my deletion attempts:

Log.e("LOOK HERE: ", String.format(Locale.US, "Your Application %s delete this file (%s)", (fileOrDirectory.canWrite() ? "can" : "can NOT"), fileOrDirectory.getName()));

And have always gotten back Your Application can NOT delete this file (path.to.file). It seems that I do not have the authorization to delete files on the SD card, even though I can through the Windows file browser.

So, is an application allowed to delete the contents of the SD card? If so, how does one go about doing this? How about a method to just format the SD card, I would take that as well.

Also, please don't ask "why do you want to do this" ... I just do.