How can I travel overseas as an E-2 visa holder with a pending EB-5 application?

If you filed for an adjustment of status, then you would need an advance parole to reenter. But if not, then you should be able to travel with the E-2, provided you can convince the customs officer upon return that you will not be entering for the purpose of adjusting status.

Have you filed the I-485? If yes, need a travel permit.

The problem with E-2 visa is that it is a non-immigrant visa that does not allow dual intent for immigrating, although some have argued and USCIS has accepted that it should be a dual intent visa at times. If you have the actual Visa in your passport that has not expired and your I-526 was filed with the Consular processing option (indicating that you will apply for immigrant visa outside of the U.S.), you should be okay traveling with the E-2 visa as long as you have not violated your visa requirements. If you are no longer conducting business under E-2 and have filed the I-485 concurrently or based on your pending I-526 within the U.S., then you should wait until your advance parole travel permit (that was filed along with your I-485 application) is approved before you travel.

The E-2 Treaty Investor status is a less stringent non-immigrant visa category than many others. However, the USCIS usually expects that a holder of an E-2 status will not adjust status inside the US to a green card. If an E-2 holder also has a green card process like the EB-5 already underway, then it is possible to argue that the E-2 holder will not adjust status to the EB-5 green card, and thus can continue to comply with the E-2 rules. It is advisable to consult with experienced immigration counsel before traveling outside of the US when in such a circumstance.

The answer depends on whether you filed for adjustment of status? If you did, then no, you cannot use your E-2 visa to travel.