TWA has good and accurate comments.

If you are crossing into Jordan via the Allenby bridge you need to obtain a VISA in advance, before you leave your home country. It is not issued at the border.

I hope you are not planning on driving a vehicle into Jordan. Israeli rentals can not be taken to Jordan--nor can Jordanian rentals be taken to Israel.

BTW you may be flying into TLV, but in reality you are landing approx. 20-30 minutes outside the city and 30-40 minutes outside of Jerusalem. In other words, the airport is on the highway between the two cities.