Shulchan Arukh, Orach Chayim 601/שולחן ערוך·אורח חיים תר״א

1The order of the 2nd day of Rosh HaShana and in it is 2 paragraphs On the 2nd day (we pray like the 1st day) (Tur) and we read from "And God tested Abraham" (Bereshis 22:1) until the end of the portion (Bereshis 22:24). The Maftir reading is the same as yesterday. And the Haftarah is in Yirmiyah (Jeremiah) "Thus Spoke Hashem: (the Nation) found favor in the desert" (Jeremiah 31:2) until "The son, precious to me, is Efrayim" (Jeremiah 31:20). On Motzei Rosh HaShana, we make Havdala like on Motzei Shabbos; however, we do not make a blessing on the spices or on the flame.

2Even in the Land of Israel, we make Rosh HaShana two days.