I will need go from Newark airport to Philadelphia Airport.
What is best way to do that trip?
I will land at Newark around 9 PM
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If by best you mean the quickest and easiest, reserving a car/limo service to pick you up at your arrivals terminal at Newark Airport and drop you off of at the precise location you require at the Philadelphia Airport would be the best. Going rates (2018) for a private sedan from Newark airport to Philadelphia Airport are $220-$275 plus a 20% tip for the driver.
Reference source: My personal knowledge from being involved in the car/limo service business in the New Jersey area for over 25 years.
Disclosure: I own a car/limo service, but I do not provide transportation between Newark Airport and Philadelphia Airport.
There are several options for getting from EWR to PHL.
One quite simple is to hire a car in Newark one-way and drive to Philadelphia airport - it's about 2 hours drive (Route 1 south and onto I-95 south straight to PHL).
Option two is to take Amtrak train from EWR airport (there's free shuttle from the terminal to the train station) to Philadelphia 30th street station and there change to SEPTA train to the airport. Amtrak takes about 45-60 minutes, plus the SEPTA train another about 25 minutes. Amtrak is quite expensive though, depending on day/time, it may cost you $60-100 per person plus the SEPTA train to the airport.
If you want to save some more money, you can take New Jersey Transit train to Trenton. There change to SEPTA line to Philadelphia 30th street station and there change to SEPTA train to the airport. It'll take you about 2 hours to Phila 30th street station with another about 25 minutes to the PHL airport - but it can be significantly cheaper than amtrak - probably, about $35-40 per person total cost.
Especially if there is more than one person travelling, cost-wise it could be best to just hire a car. Depending on the day, it would cost probably under $100 (one-way is always more expensive).
P.S. I have done similar trips quite a few times when I lived in Philadelphia, but I left it in 2000. The options are probably the same, but the prices are certainly different.