Hi, a transfer is needed. Firstly, you could take the Airport Express Line 6 to its terminal Tianhe Dasha, which is near the station. Then, I think you could take a taxi to the East Station which only cost about 8yuan. Or, you could take a taxi to the station directly, the fare should around 100yuan.

Well, take the Airport Express bus Line 1 to its terminal Guangzhou Railway Station, costs 16yuan. Then, take the subway Line2 there. From Guangzhou Railway Station to Gongyuanqian, costs 2yuan. Thirdly, at the Guangyuanqian Station, tranfer to subway Line1 to Guangzhou East Railway Station, also costs 2yuan.

No need to hava any transfer! You could take the Airport Express Line 6 to its terminal, where the East railway station is just located~