You need a Route: Plus High Speed ticket; your options are:
Anytime Day Return £37.80
Off Peak Return £37.20
Off Peak Day Return £34.80
Obviously only the Off Peak Return is valid to return the next day (this ticket is valid at or after 0930); if you need to travel outside the valid times for this ticket then two singles would be needed.
Really, you should be offered a Route: Not valid on HS1 ticket with an excess for the outbound leg (with the excess priced at half the difference), but by all accounts Southeastern staff are strangely reluctant to do this.
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edit: You'd be better off with an Ealing Broadway-Bexhill Off Peak Return, routed +Any Permitted and priced £31.20 (restriction 4B), valid to start short from London. There may be better tickets.