Can 18psi water source run a 20" Big Blue Sediment filter without pump?
It depends on which model and what rate of flow you are using at the time.  The manufacturer's spec sheet has the details:
Big Blue Filter Specs
See the section titled

SPECIFICATIONS AND PERFORMANCE

In the table there look at the right-hand column for INITIAL ∆P.  Also refer to the graph:  PRESSURE DROP VS FLOW RATE
EDIT:
In your comment you said:

My point is. Compared to with and without any filter. The flow rate
can change due to changing in pressure via the filter, right? This is
my original question not directly answeree

No, you asked about pressure not flow rate.  Specifically you asked:

What will happen to my 18psi pressure? Will it turn it to 15psi or
maybe 10psi?

This is answered by the specs from the filter manufacturer.  This does not address flow rate as that is NOT determined by the filter.
To specifically answer the questions you raised in your post as well as the question you asked in your comments:

The PRESSURE will drop because of the insertion of any filter.  How much depends on the filter, its condition, the flow rate, and other factors.
The FLOW is determined by the source (i.e. the pump or the municipal supply) and is not directly affected by the filter.

Check the specs on your pump (assuming you have a pump as you didn't say) and you will see graphs such as this one that show how the pump's flow is affected by the pressure (i.e. the &quot;head&quot;).
Sample Flow vs. Head Graph
In other words, it depends.