See my other answer first which is a lot simpler!!

This is Kenji's answer ("ıɾuǝʞ" above), reworked painfully and explained by a complete noob (myself) for other complete noobs. I also added an important workaround in the last step:

Better later than never, here is a hack to achieve this:

1. Open Terminal.app and enter the following command:

   sudo ifconfig lo0 alias 127.0.0.2/32
   

2. Plug in your usb drive

3. Go to System Preferences / Sharing

4. Open the lock in the bottom-left corner

   (Whenever asked for your password, go ahead and enter it)

5. Tick "File Sharing" on the left pane.

6. Tick Options button and activate both SMB and AFP
7. Click the + sign in the middle pane (titled "Shared Folders") and locate your USB drive. Create a folder (e.g. "time-machine-macbook") and select it to create the shared folder.

8. Then, add a destination backup (Time Machine will see it as a network share), using the following command in Terminal.app:

   sudo tmutil setdestination -a "smb://user:[email protected]/time-machine-macbook"
   

   (If you get an error that Terminal needs more access rights to your disk, then go ahead and follow the instructions of the error message to give such rights and repeat this step.)

   You can check if it's ok with the following Terminal command:

   tmutil  destinationinfo
   

   And you will get the following reply on your Terminal window:

   ==================================================
   Name          : time-machine4
   Kind          : Network
   URL           : smb://kenji@realserver._smb._tcp.local./time-machine
   ID            : D820D053-C74A-4A06-A7E1-E60C8EA7934F
   ====================================================
   Name          : time-machine-macbook
   Kind          : Network
   URL           : smb://[email protected]/time-machine-macbook
   Mount Point   : /Volumes/time-machine-macbook
   ID            : F707BD0B-64DF-4DB6-A3B7-824470FB5EB2
   

9. Then start a backup with Terminal command:

   tmutil startbackup
   

10. Terminal command mount will show (among others) something like:

    /dev/disk3s1 on /Volumes/time-machine-usb (apfs, local, nodev, nosuid, journaled, noowners)
    //[email protected]/time-machine-macbook on /Volumes/time-machine-macbook (smbfs, nobrowse)`
    

11. You can see detailed progress with Terminal command:

    tmutil status
    

    Where you'll get something like:

    Backup session status:
    {
        BackupPhase = Copying;
        ClientID = "com.apple.backupd";
        DateOfStateChange = "2018-06-28 17:38:21 +0000";
        DestinationID = "F707BD0B-57DC-4DB6-A3B7-824470FB5EB2";
        DestinationMountPoint = "/Volumes/Time Machine Backups";
        FirstBackup = 1;
        Percent = "0.08711567546702646";
        Progress =     {
            TimeRemaining = 32679;
            "_raw_totalBytes" = 355694600192;
            bytes = 34429528173;
            files = 887351;
            totalBytes = 391264060211;
            totalFiles = 2922384;
        };
        Running = 1;
        Stopping = 0;
        "_raw_Percent" = "0.09679519496336274";
    }
    

    Of course you can also have a rough idea of the progress by opening Time Machine where you will get the total MB copied as well as a calculation of the time remaining.

    In Kenji's case, near 1000000 files were done in about two hours (USB2 disk), versus more than 8 hours necessary via Wi-Fi. My results were quite faster with a USB3 disk. In 2h I had backed-up more than 500MB.

12. Next step, when backup is finished, plug the usb drive to your realserver and copy the sparsebundle over the "uncompleted one" (or in the shared folder). Of course, Time Machine should be disabled during this step to prevent mounting a partially copied sparsebundle (and maybe corrupting it). I have used an apfs drive to benefit of snapshots (to be able to revert to a previous "backupdb" in case of sparsebundle corruption, not tested yet)

13. If #12 above doesn't work and Time Machine cannot backup TO the really-networked drive (but may possibly be able to read it), then the workaround is to copy the backup bundle inside a new sparsebundle! Awkwardly, Time Machine can use networked sparsebundles as backup destinations (but not it's own backupbundle!).

14. Have your drive connected via USB (for speed) and use Disk Utility to create inside it a sparsebundle with the necessary size to fit all your backup. This might take a few hours depending on the size and speed, so choose to do it overnight. If you don't have enough drive space, then unfortunately you should remove your previously created backup and re-create it later on from the beginning inside the new sparsebundle.

15. To create the new spasebundle, open Disk Utility, click File/New Image/Blank Image and in the pop-up window add a filename (e.g. BackupBundle.dmg), no tags, choose to be inside your USB drive root, choose a volume name (e.g. BackupBundle), size larger than your HD size, format definitely Mac OS Extended (Journaled), no encryption, Single partition - Apple Partition Map, and finally sparse bundle disk image. Check again your selected size (sometimes it gets back to default) and hit save.

16. Hours later, when it's over, you may test your new sparsebundle over the network. Connect your drive to your router, open Finder, and double click your BackupBundle.sparsebundle. You should see a new disk on the sidebar and on your desktop called BackupBundle. Then open Terminal and see if the sparsebundle can be added as a backup destination. If not, then you can set it manually via Terminal.app:

    sudo tmutil setdestination -a  "/Volumes/BackupBundle"
    

17. After all this, you can copy Time Machine's backupbundle inside your BackupBundle.sparsebundle. This will also take hours, so you may want to do it the next night. Alternatively, if you didn't have room in steps 14-15 and you had to delete it, you can set Time Machine to use it as backup destination when connected via USB and then again after the first full backup is completed to select the same destination via network.

Good luck!

For Posterity, this appears to have been resolved at some point between 14.4.1 and 14.5. But is not in the release notes that I could find. Potentially an unexpected consequence related to another issue.

Because your Shared drive is not a TimeMachine enabled shared volume.

TimeMachine have special requirements using AFP as pointed out by gabedwrds thus thoses (eg. AFP Replay Cache) are not necessarily included with "OSX Client".

You should enable a "TimeMachine Server" in order to share an external disk accross the network.

You may try using the Terminal if you are not prepared to buy "Server.app". But you're talking about data backup therefore you want to be sure about consistency and recoverability ! Other backup solutions such as the excellent "Carbon Copy Cloner can achieve this without the "Server.app" and you may get free of charges similar results by using the rsync command from the terminal or using Automator.app…

If you don't care about using an unsupported solution and you are willing to take the risk of being in the so called "poo" :

• Either show unsupported network volumes :

defaults write com.apple.systempreferences TMShowUnsupportedNetworkVolumes 1

And then have a look in your TimeMachine system preferences…

• Or inputing the shared volume name manually therefore in your case type in the terminal :

sudo tmutil setdestination /Volumes/MBA\ TM

Then start your first backup :

tmutil startbackup

How to make Time Machine backups over network without OS X server?