Timekoin is not trying to solve anything related to bitcoin. It is a different way to use digital online encrypted currency. The website has technical documents to read, but the concepts and implementations can not be easily summarized into a few sentences.
Transactions and Currency creation are two separate process. So transactions can be processed like clockwork every 5 minutes. Currency creation is created in slow, gradually growing amounts. Unlike bitcoin, where currency creation stalls transaction recording and vast amounts of electricity are needed to have peers compete against each other in a lottery fashion.
Similarity to Bitcoin:
A. Uses open p2p network to replicate transactions
B. Decentralized database of history transactions
C. Public viewable by anyone
Difference to Bitcoin:
A. Uses 1536 bit transaction encryption vs 256 bit for bitcoin
B. Transactions are protected by both RSA encryption and SHA hashing in a design modeled after naturally occurring quantum entanglement.
C. Transactions do not depend on currency creation, the network can function without any currency being created as long as currency exist to spend
D. Currency creation is a shared process among all server operators that participate, so there is no spending CPU/Electricity to fight over who creates currency.
E. Currency creation can dynamically expand and contract as the network needs the currency and is not limited to who can afford the most processing power.
F. Software is just an implementation of a concept, so anyone can create any kind of application or device to interface with the Timekoin network as long as it follows the rules of the network.
G. There is no cost to transactions, no micro fees, no decimal point transactions, everything is whole numbers.
H. The Timekoin concept for digital encrypted currency is very easy to understand, so easy that many people over-think it.
I. Built from the ground up with security as the guiding factor for both transactions and network health.
I could go on about the difference, but the website has a lot more to offer in this regard. http://timekoin.org/