If you make a single transaction including the bitcoin from both addresses, then that is a fairly strong indication that both addresses are part of the same wallet.

If you make two separate transactions, one from each address, then the answer is more complicated. If both transactions are to the same deposit address, and that address can easily be identified as belonging to an exchange, then that is a fairly strong indication that the same person controls both addresses, although not necessarily they are part of the same wallet. Even if the exchange allows you to generate a new deposit address for your two transactions, then obviously they will still know that you own both addresses, and may or may not share that information with other parties.

Further, you need to be careful about future use. You should obviously never use those two addresses again. If you leave change over from either of the transactions, then you have to be careful not to link that change to the other address as well in any future transactions.

All of this is based on blockchain evidence only, but there are other things you need to consider too. Since you said you are running Electrum, you will connect to a node to update your balances and broadcast transactions. That node will see requests for the balance of those two addresses and your two transactions being broadcast all from the same IP, and so could be relatively certain they are part of the same wallet.