As you two websites are on different drives (E and F), but on the same server (presumably), you can do this by having Publication specific settings within your cd_storage_conf.xmlcd_storage_conf.xml
file.
<?xml version="1.0" encoding="UTF-8"?>
<Configuration Version="6.1" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="schemas/cd_storage_conf.xsd">
<Global>
...
<Storages TempFileSystemTransactionLocation="F:\Temp" >
...
<Storage Class="com.tridion.storage.filesystem.FSDAOFactory" Type="filesystem" Id="IISFileSystem" defaultStorage="false" defaultFilesystem="false">
<Root Path="F:\" />
</Storage>
<Storage Type="filesystem" Class="com.tridion.storage.filesystem.FSDAOFactory" Id="Website2_IISFileSystem" defaultFilesystem="false">
<Root Path="E:\website2" />
</Storage>
</Storages>
</Global>
<ItemTypes cached="true" defaultStorageId="sqlServer">
<Item cached="true" storageId="IISFileSystem" typeMapping="Page" />
<Item cached="true" storageId="IISFileSystem" typeMapping="Binary" />
<!-- Website 2 Publication specific -->
<Publication Id="99" defaultStorageId="sqlServer" cached="true">
<Item cached="true" storageId="Website2_IISFileSystem" typeMapping="Page" />
<Item cached="true" storageId="Website2_IISFileSystem" typeMapping="Binary" />
<!-- any other item mappings you need -->
</Publication>
</ItemTypes>
</Configuration>
You will not need another Deployer (or Publishing Target) this way.
(*Obviously you will need to merge the Publication specific settings in to your own cd_storage_conf.xml
file, as you will possibly have other configuration items in there.)