So where do I enter my single member LLC details (EIN, etc) if I file Schedule E under rental income and royalties?

[AnthonyC]

You don't enter these LLC details for tax return reporting purposes for Schedule E.  A single member LLC is considered a disregarded entity by the IRS, which means that all tax reporting is done under the owner's taxpayer identification number.  This doesn’t mean you can’t also have an EIN for a single-member LLC as there are cases where one can be required (for certain employment or excise tax issues or possibly state law requirements for opening bank accounts), but for tax return reporting purposes everything will flow to the owner’s SSN.

"For federal income tax purposes, a single-member LLC classified as a disregarded entity generally must use the owner's social security number (SSN) or EIN for all information returns and reporting related to income tax"

See this IRS Link for more information - Single Member Limited Liability Companies