Briefly and shortly are easily confused. While brief and short are often synonymous (as you can read here), briefly and shortly have very different meanings.
Briefly means for a short time.
She appeared briefly in an Italian film.
In Britain he worked briefly as a veterinarian.
We spoke briefly about the weather.
Shortly means soon and indicates a point in time.
Shortly after her exam, she moved to Paris.
I’ll be with you shortly.
The following message should not worry you too much:
The landlord will briefly cut off electricity in the building.
This means that you will be without electricity for a short time.
However, if you get the following message, you might worry:
The landlord will shortly cut off electricity in the building.
This implies that you may not have time to prepare for the power cut.
To sum up:
Briefly tells us that something lasts for a short time.
Shortly indicates a short time before or after something.
I’ll see you briefly means that I will see you for a short time.
I’ll see you shortly means that I will see you very soon.
As I mentioned above, you can read about the words brief and short here.