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You don't need to pay customs tax on the laptop as Israel doesn't have customs on laptops, but you will need to pay VAT on it, which is 17% of the total cost of the item, if its value is greater than 75$ US.
As you don't plan on leaving your own laptop in Israel you are not importing it and shouldn't pay anything for it. However, I don't know what is the process for it and you would probably need to declare it to the customs officer and ask them of the proper procedure.
Take note that when importing items to Israel through the post or a delivery service, the total value of the item includes any postage and delivery fees, not only for VAT but also for customs tax. While I don't think it should, it might be that the delivery fees in your country will be added to the value of the item if they appear on the receipt which will be used to prove the items' value.