actually no difference

From 现代汉语词典(www.51240.com/cidian/)：

了解
①知道得清楚：只有眼睛向下,才能真正～群众的愿望和要求。 ②打听；调查：先去～情况ㄧ这究竟是怎么回事？你去～一下。

知道
1.谓通晓天地之道,深明人世之理。 2.认识道路。 3.晓得,谓对事物有所了解﹑认识。 4.公文用语。犹知悉。多见于诏令。 5.犹厉害。

Chinese is Hieroglyphic so I think you can understand the difference from the word itself
了解——了：it means something had been down eg:我吃饭了
解—-know eg:解释(explaining.)
so maybe you can take it as I have understand it

as 明白
明—-it from 日 and 月 sun and moon means light,very bright
白—-means white
so from this word we can feel the feeling that when I am not very clear to see but suddenly some ray of light so it become clear .
there is a Chinese idioms also have the same meaning 恍然大悟(huang ran da wu )

明白:It just means"understand"but
了解:It has two meanings (1).understand;(2).In this situation that somebody says something that you don't know,you could say"我会去了解一下".It means you'll find some informations about that,like"to involve",and "touch on". So you see there two different meanings about了解,one is the same as 明白,but the others is different.